Л. Искауриаза, Г. А. Серёгин, В. Шверак, “$L_{3,\infty}$-решения уравнений Навье–Стокса и обратная единственность”, УМН, 58:2(350) (2003), 3–44; Russian Math. Surveys, 58:2 (2003), 211

RUS ENG

ЖУРНАЛЫ ПЕРСОНАЛИИ ОРГАНИЗАЦИИ КОНФЕРЕНЦИИ СЕМИНАРЫ ВИДЕОТЕКА ПАКЕТ AMSBIB

JavaScript is disabled in your browser. Please switch it on to enable full functionality of the website

	Общая информация
	Последний выпуск
	Архив
	Импакт-фактор
	Подписка
	Правила для авторов
	Лицензионный договор
	Загрузить рукопись
	Историческая справка

	Поиск публикаций
	Поиск ссылок

	RSS
	Последний выпуск
	Текущие выпуски
	Архивные выпуски
	Что такое RSS

УМН:
Год:
Том:
Выпуск:
Страница:
	Найти

Персональный вход:
Логин:
Пароль:
	Запомнить пароль
	Войти
	Забыли пароль?
	Регистрация

УМН, 2003, том 58, выпуск 2(350), страницы 3–44 (Mi umn609)

Эта публикация цитируется в 339 научных статьях (всего в 339 статьях)

$L_{3,\infty}$-решения уравнений Навье–Стокса и обратная единственность

Л. Искауриаза^a, Г. А. Серёгин^b, В. Шверак^c

^a Universidad del Pais Vasco-Euskal Herriko Unibertsitatea, Dipartimento di Matematicas
^b Санкт-Петербургское отделение Математического института им. В. А. Стеклова РАН
^c University of Minnesota, School of Mathematics

Аннотация: Показано, что $L_{3,\infty}$-решения задачи Коши для трехмерных уравнений Навье–Стокса являются гладкими.
Библиография: 46 названий.

DOI: https://doi.org/10.4213/rm609

Полный текст: PDF файл (480 kB)

Список литературы: PDF файл HTML файл

Англоязычная версия:
Russian Mathematical Surveys, 2003, 58:2, 211–250

Реферативные базы данных:

УДК: 517.9
MSC: Primary 35Q30; Secondary 35B65, 35D10, 35A05, 35K05, 35K60, 35B60, 76D05
Поступила в редакцию: 15.02.2003

Образец цитирования: Л. Искауриаза, Г. А. Серёгин, В. Шверак, “$L_{3,\infty}$-решения уравнений Навье–Стокса и обратная единственность”, УМН, 58:2(350) (2003), 3–44; Russian Math. Surveys, 58:2 (2003), 211–250

Цитирование в формате AMSBIB

\RBibitem{EscSerSve03}

\by Л.~Искауриаза, Г.~А.~Серёгин, В.~Шверак

\paper $L_{3,\infty}$-решения уравнений Навье--Стокса и обратная единственность

\jour УМН

\yr 2003

\vol 58

\issue 2(350)

\pages 3--44

\mathnet{http://mi.mathnet.ru/umn609}

\crossref{https://doi.org/10.4213/rm609}

\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1992563}

\zmath{https://zbmath.org/?q=an:1064.35134}

\adsnasa{http://adsabs.harvard.edu/cgi-bin/bib_query?2003RuMaS..58..211E}

\transl

\jour Russian Math. Surveys

\yr 2003

\vol 58

\issue 2

\pages 211--250

\crossref{https://doi.org/10.1070/RM2003v058n02ABEH000609}

\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000184540100001}

\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-0042154193}

Образцы ссылок на эту страницу:

http://mi.mathnet.ru/umn609

https://doi.org/10.4213/rm609

http://mi.mathnet.ru/rus/umn/v58/i2/p3

ОТПРАВИТЬ:

Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

Эта публикация цитируется в следующих статьяx:

G. A. Seregin, V. Šverak, “On smoothness of suitable weak solutions to the Navier–Stokes equations”, Краевые задачи математической физики и смежные вопросы теории функций. 34, Зап. научн. сем. ПОМИ, 306, ПОМИ, СПб., 2003, 186–198 ; J. Math. Sci. (N. Y.), 130:4 (2005), 4884–4892
G. A. Seregin, “Remarks on regularity of weak solutions to the Navier–Stokes equations near the boundary”, Краевые задачи математической физики и смежные вопросы теории функций. 33, Зап. научн. сем. ПОМИ, 295, ПОМИ, СПб., 2003, 168–179 ; J. Math. Sci. (N. Y.), 127:2 (2005), 1915–1922
О. А. Ладыженская, “Шестая проблема тысячелетия: уравнения Навье–Стокса, существование и гладкость”, УМН, 58:2(350) (2003), 45–78 ; O. A. Ladyzhenskaya, “Sixth problem of the millennium: Navier–Stokes equations, existence and smoothness”, Russian Math. Surveys, 58:2 (2003), 251–286
Berselli L.C., Galdi G.P., “On the space-time regularity of $C(0,T;L^n)$-very weak solutions to the Navier–Stokes equations”, Nonlinear Anal., 58:5-6 (2004), 703–717
Kim H., Kozono H., “Interior regularity criteria in weak spaces for the Navier–Stokes equations”, Manuscripta Math., 115:1 (2004), 85–100
G. A. Seregin, T. N. Shilkin, V. A. Solonnikov, “Boundary partial regularity for the Navier–Stokes equations”, Краевые задачи математической физики и смежные вопросы теории функций. 35, Зап. научн. сем. ПОМИ, 310, ПОМИ, СПб., 2004, 158–190 ; J. Math. Sci. (N. Y.), 132:3 (2006), 339–358
Seregin G., “On smoothness of $L_{3,\infty}$-solutions to the Navier–Stokes equations up to boundary”, Math. Ann., 332:1 (2005), 219–238
Feireisl E., Novotný A., Petzeltová H., “On a class of physically admissible variational solutions to the Navier–Stokes-Fourier system”, Z. Anal. Anwendungen, 24:1 (2005), 75–101
Kang K., Lee J., “On regularity criteria in conjunction with the pressure of the Navier–Stokes equations”, Int. Math. Res. Not., 2006, 80762, 25 pp.
W. Zajączkowski, G. A. Seregin, “A sufficient condition of local regularity for the Navier–Stokes equations”, Краевые задачи математической физики и смежные вопросы теории функций. 37, Зап. научн. сем. ПОМИ, 336, ПОМИ, СПб., 2006, 46–54 ; J. Math. Sci. (N. Y.), 143:2 (2007), 2869–2874
A. Mahalov, B. Nicolaenko, T. N. Shilkin, “$L_{3,\infty}$-solutions to the MHD equations”, Краевые задачи математической физики и смежные вопросы теории функций. 37, Зап. научн. сем. ПОМИ, 336, ПОМИ, СПб., 2006, 112–132 ; J. Math. Sci. (N. Y.), 143:2 (2007), 2911–2923
A. S. Mikhailov, T. N. Shilkin, “$L_{3,\infty}$-solutions to the 3D-Navier–Stokes system in the domain with a curved boundary”, Краевые задачи математической физики и смежные вопросы теории функций. 37, Зап. научн. сем. ПОМИ, 336, ПОМИ, СПб., 2006, 133–152 ; J. Math. Sci. (N. Y.), 143:2 (2007), 2924–2935
G. A. Seregin, “Estimates of suitable weak solutions to the Navier–Stokes equations in critical Morrey spaces”, Краевые задачи математической физики и смежные вопросы теории функций. 37, Зап. научн. сем. ПОМИ, 336, ПОМИ, СПб., 2006, 199–210 ; J. Math. Sci. (N. Y.), 143:2 (2007), 2961–2968
Г. А. Серегин, “Новая версия условия Ладыженской–Проди–Серрина”, Алгебра и анализ, 18:1 (2006), 124–143 ; G. A. Seregin, “New version of the Ladyzhenskaya–Prodi–Serrin condition”, St. Petersburg Math. J., 18:1 (2007), 89–103
Zhang Qi, “Local estimates on two linear parabolic equations with singular coefficients”, Pacific J. Math., 223:2 (2006), 367–396
Escauriaza L., Kenig C.E., Ponce G., Vega L., “Decay at infinity of caloric functions within characteristic hyperplanes”, Math. Res. Lett., 13:2-3 (2006), 441–453
Germain P., “Multipliers, paramultipliers, and weak-strong uniqueness for the Navier–Stokes equations”, J. Differential Equations, 226:2 (2006), 373–428
Gustafson S., Kang Kyungkeun, Tsai Tai-Peng, “Regularity criteria for suitable weak solutions of the Navier–Stokes equations near the boundary”, J. Differential Equations, 226:2 (2006), 594–618
Kukavica I., “Pressure integrability conditions for uniqueness of mild solutions of the Navier–Stokes system”, J. Differential Equations, 223:2 (2006), 427–441
Kukavica I., Ziane M., “One component regularity for the Navier–Stokes equations”, Nonlinearity, 19:2 (2006), 453–469
Grujić Z., Zhang Qi S., “Space-time localization of a class of geometric criteria for preventing blow-up in the 3D NSE”, Comm. Math. Phys., 262:3 (2006), 555–564
Zhou Yong, “On a regularity criterion in terms of the gradient of pressure for the Navier–Stokes equations in $\mathbb R^N$”, Z. Angew. Math. Phys., 57:3 (2006), 384–392
Zhou Yong, “On regularity criteria in terms of pressure for the Navier–Stokes equations in $\mathbb R^3$”, Proc. Amer. Math. Soc., 134:1 (2006), 149–156
Dongho Chae, “Nonexistence of asymptotically self-similar singularities in the Euler and the Navier–Stokes equations”, Math Ann, 338:2 (2007), 435
Г. А. Серёгин, “О локальной регулярности подходящих слабых решений уравнений Навье–Стокса”, УМН, 62:3(375) (2007), 149–168 ; G. A. Seregin, “Local regularity for suitable weak solutions of the Navier–Stokes equations”, Russian Math. Surveys, 62:3 (2007), 595–614
Chae Dongho, Kang Kyungkeun, Lee Jihoon, “On the interior regularity of suitable weak solutions to the Navier–Stokes equations”, Comm. Partial Differential Equations, 32:7-9 (2007), 1189–1207
Chae Dongho, “On the regularity conditions for the Navier–Stokes and related equations”, Rev. Mat. Iberoam., 23:1 (2007), 371–384
Seregin G., Zajaczkowski W., “A sufficient condition of regularity for axially symmetric solutions to the Navier–Stokes equations”, SIAM J. Math. Anal., 39:2 (2007), 669–685
Kukavica I., Ziane M., “Navier–Stokes equations with regularity in one direction”, J. Math. Phys., 48:6 (2007), 065203, 10 pp.
Struwe M., “On a Serrin-type regularity criterion for the Navier–Stokes equations in terms of the pressure”, J. Math. Fluid Mech., 9:2 (2007), 235–242
Hou Th.Y., Li R., “Nonexistence of locally self-similar blow-up for the 3D incompressible Navier–Stokes equations”, Discrete Contin. Dyn. Syst., 18:4 (2007), 637–642
Gustafson S., Kang Kyungkeun, Tsai Tai-Peng, “Interior regularity criteria for suitable weak solutions of the Navier–Stokes equations”, Comm. Math. Phys., 273:1 (2007), 161–176
Seregin G., “Navier–Stokes equations: almost $L_{3,\infty}$-case”, J. Math. Fluid Mech., 9:1 (2007), 34–43
Tao T., “A quantitative formulation of the global regularity problem for the periodic Navier–Stokes equation”, Dyn. Partial Differ. Equ., 4:4 (2007), 293–302
Vasseur A.F., “A new proof of partial regularity of solutions to Navier–Stokes equations”, NoDEA Nonlinear Differential Equations Appl., 14:5-6 (2007), 753–785
Colliander J., “On blowup solutions of NLS with low regularity initial data”, Harmonic Analysis, Partial Differential Equations, and Related Topics, Contemporary Mathematics Series, 428, 2007, 43–50
Kenig C.E., “Some recent applications of unique continuation”, Recent Developments in Nonlinear Partial Differential Equations, Contemporary Mathematics Series, 439, 2007, 25–56
Suzuki T., “On partial regularity of suitable weak solutions to the Navier–Stokes equations in unbounded domains”, Manuscripta Math., 125:4 (2008), 471–493
Wang Changyou, “Heat flow of harmonic maps whose gradients belong to $L^n_xL^\infty_t$”, Arch. Ration. Mech. Anal., 188:2 (2008), 351–369
Chen Qionglei, Miao Changxing, Zhang Zhifei, “On the regularity criterion of weak solution for the 3D viscous magneto-hydrodynamics equations”, Comm. Math. Phys., 284:3 (2008), 919–930
Fan J., Ozawa T., “Regularity criterion for weak solutions to the Navier–Stokes equations in terms of the gradient of the pressure”, J. Inequal. Appl., 2008, 412678, 6 pp.
Costin O., Luo G., Tanveer S., “An integral equation approach to smooth 3D Navier–Stokes solution”, Physica Scripta, T132 (2008), 014040, 9 pp.
Cao Chongsheng, Titi E.S., “Regularity criteria for the three-dimensional Navier–Stokes equations”, Indiana Univ. Math. J., 57:6 (2008), 2643–2661
Chou Kai-Seng, Du Shi-Zhong, “Estimates on the Hausdorff dimension of the rupture set of a thin film”, SIAM J. Math. Anal., 40:2 (2008), 790–823
Constantin P., “Euler and Navier–Stokes equations”, Publ. Mat., 52:2 (2008), 235–265
Merle F., Raphaël P., “Blow up of the critical norm for some radial $L^2$ super critical nonlinear Schrödinger equations”, Amer. J. Math., 130:4 (2008), 945–978
Bae Hyeong-Ohk, Choe Hi Jun, Jin Bum Ja, “Pressure representation and boundary regularity of the Navier–Stokes equations with slip boundary condition”, J. Differential Equations, 244:11 (2008), 2741–2763
Fan Jishan, Jiang Song, Ni Guoxi, “On regularity criteria for the $n$-dimensional Navier–Stokes equations in terms of the pressure”, J. Differential Equations, 244:11 (2008), 2963–2979
Cai Xiaojing, Jiu Quansen, “Weak and strong solutions for the incompressible Navier–Stokes equations with damping”, J. Math. Anal. Appl., 343:2 (2008), 799–809
Mahalov A., Nicolaenko B., Seregin G., “New sufficient conditions of local regularity for solutions to the Navier–Stokes equations”, J. Math. Fluid Mech., 10:1 (2008), 106–125
Hoff D., Tsyganov E., “Time analyticity and backward uniqueness of weak solutions of the Navier–Stokes equations of multidimensional compressible flow”, J. Differential Equations, 245:10 (2008), 3068–3094
Hou Thomas Y., Lei Zhen, Li Congming, “Global regularity of the 3D axi-symmetric Navier–Stokes equations with anisotropic data”, Comm. Partial Differential Equations, 33:9 (2008), 1622–1637
Kenig C.E., “The global behavior of solutions to critical nonlinear dispersive and wave equations”, Harmonic Analysis and Partial Differential Equations, Contemporary Mathematics, 505, 2008, 53–60
Hou Thomas Y., Lei Zhen, “On the stabilizing effect of convection in three-dimensional incompressible flows”, Comm. Pure Appl. Math., 62:4 (2009), 501–564
Zhou Yong, Fan Jishan, “Regularity criteria for the viscous Camassa-Holm equations”, Int. Math. Res. Not. IMRN, 2009, no. 13, 2508–2518
Fan Jishan, Ozawa Tohru, “Logarithmically improved regularity criteria for Navier–Stokes and related equations”, Math. Methods Appl. Sci., 32:17 (2009), 2309–2318
Yong Yan, Jiu Quan Sen, “Energy equality and uniqueness of weak solutions to MHD equations in $L^\infty(0,T;L^n(\Omega))$”, Acta Math. Sin. (Engl. Ser.), 25:5 (2009), 803–814
Robinson J.C., Sadowski W., “A criterion for uniqueness of Lagrangian trajectories for weak solutions of the 3D Navier–Stokes equations”, Comm. Math. Phys., 290:1 (2009), 15–22
Berselli L.C., “Some criteria concerning the vorticity and the problem of global regularity for the 3D Navier–Stokes equations”, Ann. Univ. Ferrara, 55:2 (2009), 209–224
V. A. Vyalov, “On the local smoothness of weak solutions to the MHD system”, Краевые задачи математической физики и смежные вопросы теории функций. 40, Зап. научн. сем. ПОМИ, 370, ПОМИ, СПб., 2009, 5–21 ; J. Math. Sci. (N. Y.), 166:1 (2010), 1–10
A. Mikhaylov, “Local regularity for suitable weak solutions of the Navier–Stokes equations near the boundary”, Краевые задачи математической физики и смежные вопросы теории функций. 40, Зап. научн. сем. ПОМИ, 370, ПОМИ, СПб., 2009, 73–93 ; J. Math. Sci. (N. Y.), 166:1 (2010), 40–52
Chae Dongho, “On the behaviors of solutions near possible blow-up time in the incompressible Euler and related equations”, Comm. Partial Differential Equations, 34:10 (2009), 1265–1286
Chen Qionglei, Miao Changxing, Zhang Zhifei, “On the uniqueness of weak solutions for the 3D Navier–Stokes equations”, Ann. Inst. H. Poincaré Anal. Non Linéaire, 26:6 (2009), 2165–2180
Dong Hongjie, Du Dapeng, “The Navier–Stokes equations in the critical Lebesgue space”, Comm. Math. Phys., 292:3 (2009), 811–827
Dong Hongjie, Pavlović N., “A regularity criterion for the dissipative quasi-geostrophic equations”, Ann. Inst. H. Poincaré Anal. Non Linéaire, 26:5 (2009), 1607–1619
Cortissoz J., “Some elementary estimates for the Navier–Stokes system”, Proc. Amer. Math. Soc., 137:10 (2009), 3343–3353
Fan J., Ozawa T., “Regularity criteria for the magnetohydrodynamic equations with partial viscous terms and the Leray-$\alpha$-MHD model”, Kinet. Relat. Models, 2:2 (2009), 293–305
Fan Jishan, Gao Hongjun, “Regularity conditions for the 3D Navier–Stokes equations”, Quart. Appl. Math., 67:1 (2009), 195–199
Zhou Yong, Gala S., “Logarithmically improved regularity criteria for the Navier–Stokes equations in multiplier spaces”, J. Math. Anal. Appl., 356:2 (2009), 498–501
Galaktionov V.A., Mitidieri E., Pohozaev S.I., “On global solutions and blow-up for Kuramoto-Sivashinsky-type models, and well-posed Burnett equations”, Nonlinear Anal., 70:8 (2009), 2930–2952
Seregin G., Šverák V., “On type I singularities of the local axi-symmetric solutions of the Navier–Stokes equations”, Comm. Partial Differential Equations, 34:2 (2009), 171–201
Doering Ch.R., “The 3D Navier–Stokes Problem”, Annu. Rev. Fluid Mech., 41 (2009), 109–128
Koch G., Nadirashvili N., Seregin G.A., Šverá k V., “Liouville theorems for the Navier–Stokes equations and applications”, Acta Math., 203:1 (2009), 83–105
Wang Keyan, “On global regularity of incompressible Navier–Stokes equations in $\mathbb R^3$”, Commun. Pure Appl. Anal., 8:3 (2009), 1067–1072
Hou Thomas Y., Lei Zhen, “On the partial regularity of a 3D model of the Navier–Stokes equ”, Comm. Math. Phys., 287:2 (2009), 589–612
Vasseur A., “Regularity criterion for 3d Navier–Stokes equations in terms of the direction of the velocity”, Appl. Math., 54:1 (2009), 47–52
Fan J., Gao H., “Two Component Regularity for the Navier–Stokes Equations”, Electronic Journal of Differential Equations, 2009, 121
Gala S., “A Remark on the Regularity for the 3D Navier–Stokes Equations in Terms of the Two Components of the Velocity”, Electronic Journal of Differential Equations, 2009, 148
Cheskidov A., Shvydkoy R., “The regularity of weak solutions of the 3D Navier–Stokes equations in $B_{\infty,\infty}^{-1}$”, Arch. Rational Mech. Anal., 195:1 (2010), 159–169
Grujić Z., Guberović R., “Localization of Analytic Regularity Criteria on the Vorticity and Balance Between the Vorticity Magnitude and Coherence of the Vorticity Direction in the 3D NSE”, Comm. Math. Phys., 2010
Cao Chongsheng, “Sufficient conditions for the regularity to the 3D Navier–Stokes equations”, Discrete Contin. Dyn. Syst., 26:4 (2010), 1141–1151
Kukavica I., “On regularity for the Navier–Stokes equations in Morrey spaces”, Discrete Contin. Dyn. Syst., 26:4 (2010), 1319–1328
Kim Jaewoo, Kim Myeonghyeon, “Local regularity of the Navier–Stokes equations near the curved boundary”, J. Math. Anal. Appl., 363:1 (2010), 161–173
Cao Chongsheng, Wu Jiahong., “Two regularity criteria for the 3D MHD equations”, J. Differ. Equations, 248:9 (2010), 2263–2274
Feireisl E., “Mathematical theory of viscous fluids: Retrospective and future perspectives”, Discrete Contin. Dyn. Syst., 27:2 (2010), 533–555
Jae-Myoung Kim, “On regularity criteria of the Navier–Stokes equations in bounded domains”, J Math Phys (N Y ), 51:5 (2010), 053102
Kyungkeun Kang, Jihoon Lee, “On the behaviour of Navier–Stokes equations near a possible singular point”, Nonlinearity, 23:12 (2010), 3187
V. Vyalov, T. Shilkin, “On the boundary regularity of weak solutions to the MHD system”, Краевые задачи математической физики и смежные вопросы теории функций. 41, Зап. научн. сем. ПОМИ, 385, ПОМИ, СПб., 2010, 18–53 ; J. Math. Sci. (N. Y.), 178:3 (2011), 243–264
A. S. Mikhaylov, “On local regularity for suitable weak solutions of the Navier–Stokes equations near the boundary”, Краевые задачи математической физики и смежные вопросы теории функций. 41, Зап. научн. сем. ПОМИ, 385, ПОМИ, СПб., 2010, 83–97 ; J. Math. Sci. (N. Y.), 178:3 (2011), 282–291
Lin F., Wang Ch., “On the uniqueness of heat flow of harmonic maps and hydrodynamic flow of nematic liquid crystals”, Chinese Annals of Mathematics Series B, 31:6 (2010), 921–938
Wang Shu, “On a New 3D Model for Incompressible Euler and Navier–Stokes Equations”, Acta Mathematica Scientia, 30:6 (2010), 2089–2102
Cai Zh., Fan J., Zhai J., “Regularity Criteria in Weak Spaces for 3-Dimensional Navier–Stokes Equations in Terms of the Pressure”, Differential and Integral Equations, 23:11–12 (2010), 1023–1033
Sugiyama Y., “epsilon-Regularity theorem and its application to the blow-up solutions of Keller-Segel systems in higher dimensions”, Journal of Mathematical Analysis and Applications, 364:1 (2010), 51–70
Gibbon J.D., “Regularity and singularity in solutions of the three-dimensional Navier–Stokes equations”, Proceedings of the Royal Society A-Mathematical Physical and Engineering Sciences, 466:2121 (2010), 2587–2604
He Cheng, Wang Yun, “Limiting case for the regularity criterion of the Navier–Stokes equations and the magnetohydrodynamic equations”, Science China-Mathematics, 53:7 (2010), 1767–1774
Yuan J., “Existence theorem and regularity criteria for the generalized MHD equations”, Nonlinear Analysis-Real World Applications, 11:3 (2010), 1640–1649
Qiu H., Du Y., Yao Zheng'an, “A blow-up criterion for 3D Boussinesq equations in Besov spaces”, Nonlinear Analysis-Theory Methods & Applications, 73:3 (2010), 806–815
Chae D., “On the Regularity Conditions of Suitable Weak Solutions of the 3D Navier–Stokes Equations”, Journal of Mathematical Fluid Mechanics, 12:2 (2010), 171–180
Killip R., Visan M., “Energy-Supercritical NLS: Critical H-S-Bounds Imply Scattering”, Communications in Partial Differential Equations, 35:6 (2010), 945–987
Qiu H., Du Y., Yao Zheng'an, “Serrin-type blow-up criteria for 3D Boussinesq equations”, Applicable Analysis, 89:10 (2010), 1603–1613
W. Zajączkowski, “A regularity criterion for axially symmetric solutions to the Navier–Stokes equations”, Краевые задачи математической физики и смежные вопросы теории функций. 41, Зап. научн. сем. ПОМИ, 385, ПОМИ, СПб., 2010, 54–68 ; J. Math. Sci. (N. Y.), 178:3 (2011), 265–273
G. A. Seregin, “Necessary conditions of potential blow up for Navier–Stokes equations”, Краевые задачи математической физики и смежные вопросы теории функций. 41, Зап. научн. сем. ПОМИ, 385, ПОМИ, СПб., 2010, 187–199 ; J. Math. Sci. (N. Y.), 178:3 (2011), 345–352
Han P., “Regularity and decay properties of weak solutions to Navier–Stokes equations in general domains”, Portugaliae Mathematica, 67:1 (2010), 57–74
Gala S., “Regularity for 3D Navier–Stokes Equations in Terms of Two Components of the Vorticity”, Electronic Journal of Differential Equations, 2010, 153
Koch G.S., “Profile Decompositions for Critical Lebesgue and Besov Space Embeddings”, Indiana Univ Math J, 59:5 (2010), 1801–1830
Kukavica I., “Partial regularity for the Navier–Stokes equations with a force in a Morrey space”, Journal of Mathematical Analysis and Applications, 374:2 (2011), 573–584
Yoshikazu Giga, Hideyuki Miura, “On Vorticity Directions near Singularities for the Navier–Stokes Flows with Infinite Energy”, Commun. Math. Phys, 2011
Jean-Yves Chemin, Isabelle Gallagher, Marius Paicu, “Global regularity for some classes of large solutions to the Navier–Stokes equations”, Ann. Math, 173:2 (2011), 983
Qian Zhang, “On the uniqueness of weak solutions for the 3D viscous magneto-hydrodynamic equations”, Nonlinear Analysis: Theory, Methods & Applications, 2011
Chongsheng Cao, Edriss S. Titi, “Global Regularity Criterion for the 3D Navier–Stokes Equations Involving One Entry of the Velocity Gradient Tensor”, Arch Rational Mech Anal, 2011
Zujin Zhang, Xinglong Wu, Ming Lu, “On the uniqueness of strong solution to the incompressible Navier–Stokes equations with damping”, Journal of Mathematical Analysis and Applications, 377:1 (2011), 414
James C. Robinson, Witold Sadowski, “On the Dimension of the Singular Set of Solutions to the Navier–Stokes Equations”, Commun. Math. Phys, 2011
G. Seregin, “A Certain Necessary Condition of Potential Blow up for Navier–Stokes Equations”, Commun. Math. Phys, 2011
Fan J., Jiang S., Nakamura G., Zhou Y., “Logarithmically Improved Regularity Criteria for the Navier–Stokes and MHD Equations”, J Math Fluid Mech, 13:4 (2011), 557–571
Gala S., “On the regularity criterion of strong solutions to the 3D Boussinesq equations”, Appl Anal, 90:12 (2011), 1829–1835
Kenig C., “Critical non-linear dispersive equations: global existence, scattering, blow-up and universal profiles”, Jpn J Math, 6:2 (2011), 121–141
Gala S., “A remark on the logarithmically improved regularity criterion for the micropolar fluid equations in terms of the pressure”, Math Methods Appl Sci, 34:16 (2011), 1945–1953
Kenig C.E., Merle F., “Radial Solutions To Energy Supercritical Wave Equations in Odd Dimensions”, Discrete and Continuous Dynamical Systems, 31:4 (2011), 1365–1381
Lei Zh., Zhang Q.S., “A Liouville theorem for the axially-symmetric Navier–Stokes equations”, J Funct Anal, 261:8 (2011), 2323–2345
Kenig C.E., Merle F., “Nondispersive Radial Solutions To Energy Supercritical Non-Linear Wave Equations, With Applications”, Amer J Math, 133:4 (2011), 1029–1065
Costin O., Luo G., Tanveer S., “Integral Formulation of 3D Navier–Stokes and Longer Time Existence of Smooth Solutions”, Commun Contemp Math, 13:3 (2011), 407–462
Kenig C.E., Koch G.S., “An alternative approach to regularity for the Navier–Stokes equations in critical spaces”, Ann Inst H Poincaré Anal Non Linéaire, 28:2 (2011), 159–187
Fan J., Jiang S., Nakamura G., “On logarithmically improved regularity criteria for the Navier–Stokes equations in R-n”, IMA J Appl Math, 76:2 (2011), 298–311
Bjorland C., Vasseur A., “Weak in Space, Log in Time Improvement of the LadyA3/4enskaja-Prodi-Serrin Criteria”, J Math Fluid Mech, 13:2 (2011), 259–269
Eduard Feireisl, Antonín Novotný, “Weak–Strong Uniqueness Property for the Full Navier–Stokes–Fourier System”, Arch Rational Mech Anal, 2012
Wendong Wang, Zhifei Zhang, “Limiting case for the regularity criterion to the 3-D Magneto-hydrodynamics equations”, Journal of Differential Equations, 2012
Tomoyuki Suzuki, “A remark on the regularity of weak solutions to the Navier–Stokes equations in terms of the pressure in Lorentz spaces”, Nonlinear Analysis: Theory, Methods & Applications, 2012
Cheng He, Daoguo Zhou, “The existence, uniqueness, and regularity for an incompressible Newtonian flow with intrinsic degree of freedom”, Math. Meth. Appl. Sci, 2012, n/a
Pigong Han, Cheng He, “Partial regularity of suitable weak solutions to the four-dimensional incompressible magneto-hydrodynamic equations”, Math. Meth. Appl. Sci, 2012, n/a
Pata V., “On the Regularity of Solutions To the Navier–Stokes Equations”, Commun Pure Appl Anal, 11:2 (2012), 747–761
Aynur Bulut, “Global well-posedness and scattering for the defocusing energy-supercritical cubic nonlinear wave equation”, Journal of Functional Analysis, 2012
Lu Li, Vladimír Šverák, “Backward Uniqueness for the Heat Equation in Cones”, Communications in Partial Differential Equations, 37:8 (2012), 1414
WENDONG WANG, ZHIFEI ZHANG, “REGULARITY OF WEAK SOLUTIONS FOR THE NAVIER–STOKES EQUATIONS IN THE CLASS L∞(BMO-1)”, Commun. Contemp. Math, 14:03 (2012), 1250020
J. D. Gibbon, “Conditional regularity of solutions of the three-dimensional Navier–Stokes equations and implications for intermittency”, J. Math. Phys, 53:11 (2012), 115608
Qiao Liu, Jihong Zhao, Shangbin Cui, “Uniqueness of weak solution to the generalized magneto-hydrodynamic system”, Annali di Matematica, 2012
Zhao J.-h., Liu Q., “Weak-Strong Uniqueness of Hydrodynamic Flow of Nematic Liquid Crystals”, Electron. J. Differ. Equ., 2012, 182
Guo Zh., Gala S., “A Regularity Criterion for the Navier–Stokes Equations in Terms of One Directional Derivative of the Velocity Field”, Anal. Appl., 10:4 (2012), 373–380
Ali H., Ammari Z., “On the Hausdorff Dimension of Singular Sets for the Leray-Alpha Navier–Stokes Equations with Fractional Regularization”, Dyn. Partial Differ. Equ., 9:3 (2012), 261–271
Bae H., Biswas A., Tadmor E., “Analyticity and Decay Estimates of the Navier–Stokes Equations in Critical Besov Spaces”, Arch. Ration. Mech. Anal., 205:3 (2012), 963–991
Escauriaza L., Kenig C.E., Ponce G., Vega L., “Uniqueness Properties of Solutions to Schrodinger Equations”, Bull. Amer. Math. Soc., 49:3 (2012), 415–442
Wei Zh., Wang Yu.-Zh., Wang Y.-X., “Logarithmically Improved Regularity Criteria for the Navier–Stokes Equations in Lorentz Spaces”, Appl. Math. Comput., 218:19 (2012), 9848–9852
Cheskidov A., Shvydkoy R., “Ill-Posedness for Subcritical Hyperdissipative Navier–Stokes Equations in the Largest Critical Spaces”, J. Math. Phys., 53:11 (2012), 115620
Dascaliuc R., Grujic Z., “Vortex Stretching and Criticality for the Three-Dimensional Navier–Stokes Equations”, J. Math. Phys., 53:11 (2012), 115613
Han P., “Interior Regularity of Weak Solutions to the Perturbed Navier–Stokes Equations”, Appl. Mat., 57:5 (2012), 427–444
Melcher Ch., “Global Solvability of the Cauchy Problem for the Landau-Lifshitz-Gilbert Equation in Higher Dimensions”, Indiana Univ. Math. J., 61:3 (2012), 1175–1200
Chemin J.-Y., Planchon F., “Self-Improving Bounds for the Navier–Stokes Equations”, Bull. Soc. Math. Fr., 140:4 (2012), 583–597
Jiří Neustupa, “A note on local interior regularity of a suitable weak solution to the Navier–Stokes problem”, DCDS-S, 6:5 (2013), 1391
Terence Tao, “Localisation and compactness properties of the Navier–Stokes global regularity problem”, Anal. PDE, 6:1 (2013), 25
Didier Jesslé, B.J.a Jin, Antonín Novotný, “Navier–Stokes–Fourier System on Unbounded Domains: Weak Solutions, Relative Entropies, Weak-Strong Uniqueness”, SIAM J. Math. Anal, 45:3 (2013), 1907
C. Bardos, M. C. Lopes Filho, Dongjuan Niu, H. J. Nussenzveig Lopes, E. S. Titi, “Stability of Two-Dimensional Viscous Incompressible Flows under Three-Dimensional Perturbations and Inviscid Symmetry Breaking”, SIAM J. Math. Anal, 45:3 (2013), 1871
Quansen Jiu, Yanqing Wang, “Remarks on partial regularity for suitable weak solutions of the incompressible Magnetohydrodynamics equations”, Journal of Mathematical Analysis and Applications, 2013
Wendong Wang, Zhifei Zhang, “On the Interior Regularity Criteria for Suitable Weak Solutions of the Magnetohydrodynamics Equations”, SIAM J. Math. Anal, 45:5 (2013), 2666
Xiaoxin Zheng, “A regularity criterion for the tridimensional Navier–Stokes equations in term of one velocity component”, Journal of Differential Equations, 2013
A.R.. Nahmod, Nataša Pavlović, Gigliola Staffilani, “Almost Sure Existence of Global Weak Solutions for Supercritical Navier–Stokes Equations”, SIAM J. Math. Anal, 45:6 (2013), 3431
Ballew J., Trivisa K., “Weakly Dissipative Solutions and Weak-Strong Uniqueness for the Navier–Stokes-Smoluchowski System”, Nonlinear Anal.-Theory Methods Appl., 91 (2013), 1–19
Hineman J.L., Wang Ch., “Well-Posedness of Nematic Liquid Crystal Flow in l-Uloc(3) (R-3)”, Arch. Ration. Mech. Anal., 210:1 (2013), 177–218
Zhao J., Liu Q., “Logarithmically Improved Blow-Up Criteria for a Phase Field Navier–Stokes Vesicle-Fluid Interaction Model”, J. Math. Anal. Appl., 405:2 (2013), 422–437
Foxall E., Ibrahim S., Yoneda Ts., “Streamlines Concentration and Application to the Incompressible Navler-Stokes Equations”, Tohoku Math. J., 65:2 (2013), 273–279
Gallagher I., Koch G.S., Planchon F., “A Profile Decomposition Approach to the l-T(Infinity)(l-X(3)) Navier–Stokes Regularity Criterion”, Math. Ann., 355:4 (2013), 1527–1559
Zhou Y., Lei Zh., “Logarithmically Improved Criteria for Euler and Navier–Stokes Equations”, Commun. Pure Appl. Anal, 12:6 (2013), 2715–2719
Chan Ch.H., Czubak M., “Non-Uniqueness of the Leray-Hopf Solutions in the Hyperbolic Setting”, Dyn. Partial Differ. Equ., 10:1 (2013), 43–77
Raphael P., “Kenig-Merle Concentration Capacity”, Asterisque, 2013, no. 352, 121–146
Zujin Zhang, Peng Li, Dingxing Zhong, “Navier–Stokes equations with regularity in two entries of the velocity gradient tensor”, Applied Mathematics and Computation, 228 (2014), 546
Zujin Zhang, “A remark on the regularity criterion for the 3D Navier–Stokes equations involving the gradient of one velocity component”, Journal of Mathematical Analysis and Applications, 2014
Bo-Qing Dong, Zhifei Zhang, “On the weak–strong uniqueness of Koch–Tataruʼs solution for the Navier–Stokes equations”, Journal of Differential Equations, 2014
J.C.. Cortissoz, J.A.. Montero, C.E.. Pinilla, “On lower bounds for possible blow-up solutions to the periodic Navier–Stokes equation”, J. Math. Phys, 55:3 (2014), 033101
Stefano Bosia, Monica Conti, Vittorino Pata, “A regularity criterion for the Navier–Stokes equations in terms of the pressure gradient”, centr.eur.j.math, 2014
Reinhard Farwig, “On regularity of weak solutions to the instationary Navier–Stokes system: a review on recent results”, Ann Univ Ferrara, 2014
Kang K., Kim J.-M., “Boundary Regularity Criteria for Suitable Weak Solutions of the Magnetohydrodynamic Equations”, J. Funct. Anal., 266:1 (2014), 99–120
Merle F., Raphael P., Szeftel J., “On Collapsing Ring Blow-Up Solutions to the MASS Supercritical Nonlinear Schrodinger Equation”, Duke Math. J., 163:2 (2014), 369–431
Jiří Neustupa, Patrick Penel, “Regularity of a Weak Solution to the Navier–Stokes Equations via One Component of a Spectral Projection of Vorticity”, SIAM J. Math. Anal, 46:2 (2014), 1681
Wendong Wang, Zhifei Zhang, “On the interior regularity criteria and the number of singular points to the Navier–Stokes equations”, JAMA, 123:1 (2014), 139
Stefano Bosia, Vittorino Pata, J.C.. Robinson, “A Weak-L p Prodi–Serrin Type Regularity Criterion for the Navier–Stokes Equations”, J. Math. Fluid Mech, 2014
J.D. Gibbon, D.A. Donzis, Anupam Gupta, R.M. Kerr, Rahul Pandit, “Regimes of nonlinear depletion and regularity in the 3D Navier–Stokes equations”, Nonlinearity, 27:10 (2014), 2605
Jie Wu, Wendong Wang, “On backward uniqueness for the heat operator in cones”, Journal of Differential Equations, 2014
Jie Wu, Liqun Zhang, “Backward uniqueness for parabolic operators with variable coefficients in a half space”, Commun. Contemp. Math, 2014, 1550011
Dong H., Gu X., “Boundary Partial Regularity For the High Dimensional Navier–Stokes Equations”, J. Funct. Anal., 267:8 (2014), 2606–2637
Jiu Q., Wang Ya., “On Possible Time Singular Points and Eventual Regularity of Weak Solutions To the Fractional Navier–Stokes Equations”, Dyn. Partial Differ. Equ., 11:4 (2014), 321–343
Chae D., Tsai T.-P., “On Discretely Self-Similar Solutions of the Euler Equations”, Math. Res. Lett., 21:3 (2014), 437–447
Vialov V., “On the Regularity of Weak Solutions To the Mhd System Near the Boundary”, J. Math. Fluid Mech., 16:4 (2014), 745–769
Choi K., Vasseur A.F., “Estimates on Fractional Higher Derivatives of Weak Solutions For the Navier–Stokes Equations”, Ann. Inst. Henri Poincare-Anal. Non Lineaire, 31:5 (2014), 899–945
Chen Q., Tan Zh., Wu G., “Lps's Criterion For Incompressible Nematic Liquid Crystal Flows”, Acta Math. Sci., 34:4 (2014), 1072–1080
Jia H., Sverak V., “Local-in-Space Estimates Near Initial Time For Weak Solutions of the Navier–Stokes Equations and Forward Self-Similar Solutions”, Invent. Math., 196:1 (2014), 233–265
Wong P., “Global Wellposedness For a Certain Class of Large Initial Data For the 3D Navier–Stokes Equations”, Ann. Henri Poincare, 15:4 (2014), 633–643
Robinson J.C., Sadowski W., “A Local Smoothness Criterion For Solutions of the 3D Navier–Stokes Equations”, Rend. Semin. Mat. Univ. Padova, 131 (2014), 159–178
Cheskidov A., Shvydkoy R., “A Unified Approach To Regularity Problems For the 3D Navier–Stokes and Euler Equations: the Use of Kolmogorov's Dissipation Range”, J. Math. Fluid Mech., 16:2 (2014), 263–273
Pigong Han, “Decay Results of Higher-Order Norms for the Navier–Stokes Flows in 3D Exterior Domains”, Commun. Math. Phys, 334:1 (2015), 397
Zujin Zhang, “An almost Serrin-type regularity criterion for the Navier–Stokes equations involving the gradient of one velocity component”, Z. Angew. Math. Phys, 2015
Radu Dascaliuc, Nicholas Michalowski, Enrique Thomann, E.C.. Waymire, “Symmetry breaking and uniqueness for the incompressible Navier–Stokes equations”, Chaos, 25:7 (2015), 075402
Wang B., “Ill-Posedness For the Navier–Stokes Equations in Critical Besov Spaces (B) Over Dot(Infinity,Q) (-1)”, Adv. Math., 268 (2015), 350–372
Kim N., Kwak M., Yoo M., “Regularity Conditions of 3D Navier–Stokes Flow in Terms of Large Spectral Components”, Nonlinear Anal.-Theory Methods Appl., 116 (2015), 75–84
Ding Y., Sun X., “Uniqueness of Weak Solutions For Fractional Navier–Stokes Equations”, Front. Math. China, 10:1 (2015), 33–51
Bae H.-O., “Regularity Criterion For Generalized Newtonian Fluids in Bounded Domains”, J. Math. Anal. Appl., 421:1 (2015), 489–500
Zhaohui Dai, Xiaosong Wang, Lingrui Zhang, Wei Hou, “Blow-Up Criterion of Weak Solutions for the 3D Boussinesq Equations”, Journal of Function Spaces, 2015 (2015), 1
Zujin Zhang, Xian Yang, “On the regularity criterion for the Navier–Stokes equations involving the diagonal entry of the velocity gradient”, Nonlinear Analysis: Theory, Methods & Applications, 122 (2015), 169
Dongho Chae, “Remarks on the asymptotically discretely self-similar solutions of the Navier–Stokes and the Euler equations”, Nonlinear Analysis: Theory, Methods & Applications, 125 (2015), 251
Angkana Rüland, “On the backward uniqueness property for the heat equation in two-dimensional conical domains”, manuscripta math, 2015
Zujin Zhang, Xian Yang, “A note on the regularity criterion for the 3D Navier–Stokes equations via the gradient of one velocity component”, Journal of Mathematical Analysis and Applications, 2015
Xuanji Jia, Yong Zhou, “Ladyzhenskaya–Prodi–Serrin type regularity criteria for the 3D incompressible MHD equations in terms of 3 × 3 mixture matrices”, Nonlinearity, 28:9 (2015), 3289
Luo Yu., Tsai T.-P., “Regularity Criteria in Weak l-3 For 3D Incompressible Navier–Stokes Equations”, Funkc. Ekvacioj-Ser. Int., 58:3 (2015), 387–404
Nguyen Cong Phuc, “the Navier–Stokes Equations in Nonendpoint Borderline Lorentz Spaces”, J. Math. Fluid Mech., 17:4 (2015), 741–760
Xue L., “on the Discretely Self-Similar Solutions For the 3D Navier–Stokes Equations”, Nonlinearity, 28:10 (2015), 3695–3708
Barker T., Seregin G., “Ancient Solutions To Navier–Stokes Equations in Half Space”, J. Math. Fluid Mech., 17:3 (2015), 551–575
Bulut A., “the Defocusing Energy-Supercritical Cubic Nonlinear Wave Equation in Dimension Five”, Trans. Amer. Math. Soc., 367:9 (2015), 6017–6061
Bae H., “Existence and Analyticity of Lei-Lin Solution To the Navier–Stokes Equations”, Proc. Amer. Math. Soc., 143:7 (2015), PII S0002-9939(2015)12266-6, 2887–2892
Foias C., Jolly M.S., Lan R., Rupam R., Yang Y., Zhang B., “Time Analyticity With Higher Norm Estimates For the 2D Navier–Stokes Equations”, IMA J. Appl. Math., 80:3 (2015), 766–810
Tran Ch.V., Yu X., “Depletion of Nonlinearity in the Pressure Force Driving Navier–Stokes Flows”, Nonlinearity, 28:5 (2015), 1295–1306
Dodson B., Lawrie A., “Scattering For Radial, Semi-Linear, Super-Critical Wave Equations With Bounded Critical Norm”, Arch. Rational Mech. Anal, 218:3 (2015), 1459–1529
Flandoli F., “a Stochastic View Over the Open Problem of Well-Posedness For the 3D Navier–Stokes Equations”, Stochastic Analysis: a Series of Lectures, Progress in Probability, 68, eds. Dalang R., Dozzi M., Flandoli F., Russo F., Birkhauser Verlag Ag, 2015, 221–246
Cai X., Sun Y., “Blowup Criteria For Strong Solutions To the Compressible Navier–Stokes Equations With Variable Viscosity”, Nonlinear Anal., 29 (2016), 1–18
Lorenz J., Melo W.G., “on the Blow-Up Criterion of Periodic Solutions For Micropolar Equations in Homogeneous Sobolev Spaces”, Nonlinear Anal., 27 (2016), 93–106
Ohkitani K., “Late Formation of Singularities in Solutions To the Navier–Stokes Equations”, J. Phys. A, 49:1 (2016), 015502
Skalak Z., “a Regularity Criterion For the Navier–Stokes Equations Based on the Gradient of One Velocity Component”, J. Math. Anal. Appl., 437:1 (2016), 474–484
Ye Zh., “Remarks on the Regularity Criterion To the Navier–Stokes Equations Via the Gradient of One Velocity Component”, J. Math. Anal. Appl., 435:2 (2016), 1623–1633
Han P., “Long-Time Behavior For Navier–Stokes Flows in a Two-Dimensional Exterior Domain”, J. Funct. Anal., 270:3 (2016), 1091–1152
T. Barker, “Local boundary regularity for the Navier–Stokes equations in nonendpoint borderline Lorentz spaces”, Краевые задачи математической физики и смежные вопросы теории функций. 45, Посвящается юбилею Григория Александровича СЕРЕГИНА, Зап. научн. сем. ПОМИ, 444, ПОМИ, СПб., 2016, 15–46 ; J. Math. Sci. (N. Y.), 224:3 (2017), 391–413
Burczak J., Zajazkowski W.M., Nonlinear Anal.-Real World Appl., 31 (2016), 513–532
Liu Q., “On weak–strong uniqueness of solutions to the generalized incompressible Navier–Stokes equations”, Comput. Math. Appl., 72:3 (2016), 675–686
Tran Ch.V., Yu X., “Logarithmic improvement of regularity criteria for the Navier–Stokes equations in terms of pressure”, Appl. Math. Lett., 58 (2016), 62–68
Huang T., “Regularity and uniqueness for a class of solutions to the hydrodynamic flow of nematic liquid crystals”, Anal. Appl., 14:4 (2016), 523–536
Gala S., Ragusa M.A., “Logarithmically improved regularity criterion for the Boussinesq equations in Besov spaces with negative indices”, Appl. Anal., 95:6 (2016), 1271–1279
Yamazaki K., “On the three-dimensional magnetohydrodynamics system in scaling-invariant spaces”, Bull. Sci. Math., 140:5 (2016), 575–614
Wang L., “Uniqueness of self-similar shrinkers with asymptotically cylindrical ends”, J. Reine Angew. Math., 715 (2016), 207–230
Hsu P.-Y., Notsu H., Yoneda T., “A local analysis of the axisymmetric Navier–Stokes flow near a saddle point and no-slip flat boundary”, J. Fluid Mech., 794 (2016), 444–459
Ohkitani K., “Study of the Navier–Stokes regularity problem with critical norms”, Fluid Dyn. Res., 48:2 (2016), 021401
Gibbon J.D., “High–low frequency slaving and regularity issues in the 3D Navier–Stokes equations”, IMA J. Appl. Math., 81:2 (2016), 308–320
Gallagher I., Koch G.S., Planchon F., “Blow-up of Critical Besov Norms at a Potential Navier–Stokes Singularity”, Commun. Math. Phys., 343:1 (2016), 39–82
Yamazaki K., “Regularity Criteria of the Three-Dimensional Mhd System Involving One Velocity and One Vorticity Component”, Nonlinear Anal.-Theory Methods Appl., 135 (2016), 73–83
Bae H., Cannone M., “Log-Lipschitz Regularity of the 3D Navier–Stokes Equations”, Nonlinear Anal.-Theory Methods Appl., 135 (2016), 223–235
Shi J., Zhang Q., “Remarks on the uniqueness of weak solution for the 3D viscous magneto-hydrodynamics equations in
$${B^{1}_{\infty,\infty}}$$
B ∞ , ∞ 1”, Z. Angew. Math. Phys., 67:1 (2016), UNSP 7
Gala S., Ragusa M.A., “A regularity criterion for 3D micropolar fluid flows in terms of one partial derivative of the velocity”, Ann. Pol. Math., 116:3 (2016), 217–228
Zhang Z., Yang X., “Navier–Stokes equations with vorticity in Besov spaces of negative regular indices”, J. Math. Anal. Appl., 440:1 (2016), 415–419
Tao T., “Finite time blowup for an averaged three-dimensional Navier–Stokes equation”, J. Am. Math. Soc., 29:3 (2016), 601–674
Gala S., Ragusa M.A., “A new regularity criterion for the Navier–Stokes equations in terms of the two components of the velocity”, Electron. J. Qual. Theory Differ., 2016, no. 26, 1–9
Grujic Z., “Vortex stretching and anisotropic diffusion in the 3D Navier–Stokes equations”, Recent Advances in Partial Differential Equations and Applications, Contemporary Mathematics, 666, eds. Radulescu V., Sequeira A., Solonnikov V., Amer Mathematical Soc, 2016, 239–251
Chemin J.-Y., Zhang P., “On the critical one component regularity for 3-D Navier–Stokes system”, Ann. Sci. Ec. Norm. Super., 49:1 (2016), 131–167
Ye Zh., “Remarks on the Regularity Criterion To the 3D Navier–Stokes Equations Via One Velocity Component”, Differ. Integral Equ., 29:9-10 (2016), 957–976
Wang Ya., Wu G., Zhou D., “Refined regularity class of suitable weak solutions to the 3D magnetohydrodynamics equations with an application”, Z. Angew. Math. Phys., 67:6 (2016), 136
Zhang Z., Zhou Y., Comput. Math. Appl., 72:9 (2016), 2311–2314
Wu J., Zhang L., “The Landis–Oleinik conjecture in the exterior domain”, Adv. Math., 302 (2016), 190–230
Tran Ch.V., Yu X., “Pressure moderation and effective pressure in Navier–Stokes flows”, Nonlinearity, 29:10 (2016), 2990–3005
Bae H.-O., Kang K., Kim M., “Local Regularity Criteria of the Navier–Stokes Equations With Slip Boundary Conditions”, J. Korean. Math. Soc., 53:3 (2016), 597–621
Yamazaki K., “Regularity criteria of the 4D Navier–Stokes equations involving two velocity field components”, Commun. Math. Sci., 14:8 (2016), 2229–2252
Zhang Z., “Remarks on regularity criteria for the Navier–Stokes equations with axisymmetric data”, Ann. Pol. Math., 117:2 (2016), 181–196
Liu X.-G., Min J., Wang K., Zhang X., “Serrin's regularity results for the incompressible liquid crystals system”, Discret. Contin. Dyn. Syst., 36:10 (2016), 5579–5594
LemarieRieusset P., “Navier–Stokes Problem in the 21St Century”, Navier-Stokes Problem in the 21St Century, Crc Press-Taylor & Francis Group, 2016, 1–708
Robinson J., Rodrigo J., Sadowski W., “Three-Dimensional Navier–Stokes Equations: Classical Theory”, Three-Dimensional Navier-Stokes Equations: Classical Theory, Cambridge Studies in Advanced Mathematics, 157, Cambridge Univ Press, 2016, 1–471
Chemin J.-Y., Zhang P., Zhang Zh., “On the Critical One Component Regularity for 3-D Navier–Stokes System: General Case”, Arch. Ration. Mech. Anal., 224:3 (2017), 871–905
Seregin G., Sverak V., Nonlinear Anal.-Theory Methods Appl., 154:SI (2017), 269–296
Wang WenDong, Zhang ZhiFei, “Blow-up of critical norms for the 3-D Navier–Stokes equations”, Sci. China-Math., 60:4 (2017), 637–650
Kukavica I., Rusin W., Ziane M., “An Anisotropic Partial Regularity Criterion for the Navier–Stokes Equations”, J. Math. Fluid Mech., 19:1 (2017), 123–133
Hmidi T., Li D., “Small $\dot{B}^{-1}_{\infty , \infty}$ implies regularity”, Dyn. Partial Differ. Equ., 14:1 (2017), 1–4
Fan J., Ozawa T., “Regularity Criteria For Navier–Stokes and Related System”, Differ. Integral Equ., 30:1-2 (2017), 101–114
Pierfelice V., “The Incompressible Navier–Stokes Equations on Non-compact Manifolds”, J. Geom. Anal., 27:1 (2017), 577–617
Tran Ch.V., Yu X., “Note on Prodi-Serrin-Ladyzhenskaya type regularity criteria for the Navier–Stokes equations”, J. Math. Phys., 58:1 (2017), 011501
Lai B., Lin J., Wang Ch., “Forward Self-Similar Solutions to the Viscoelastic Navier–Stokes Equation with Damping”, SIAM J. Math. Anal., 49:1 (2017), 501–529
Ohkitani K., “Characterization of blowup for the Navier–Stokes equations using vector potentials”, AIP Adv., 7:1 (2017), 015211
Tran Ch.V., Yu X., “Regularity of Navier–Stokes flows with bounds for the pressure”, Appl. Math. Lett., 67 (2017), 21–27
Chae D., Lee J., “On the geometric regularity conditions for the 3D Navier–Stokes equations”, Nonlinear Anal.-Theory Methods Appl., 151 (2017), 265–273
Braz e Silva P., Melo W.G., Zingano P.R., “Lower Bounds on Blow-up of Solutions for Magneto-Micropolar Fluid Systems in Homogeneous Sobolev Spaces”, Acta Appl. Math., 147:1 (2017), 1–17
Ohkitani K., “Near-invariance under dynamic scaling for Navier–Stokes equations in critical spaces: a probabilistic approach to regularity problems”, J. Phys. A-Math. Theor., 50:4 (2017), 045501
Bradshaw Z., Grujic Z., “Frequency Localized Regularity Criteria for the 3D Navier–Stokes Equations”, Arch. Ration. Mech. Anal., 224:1 (2017), 125–133
Ohkitani K., “Cole-Hopf-Feynman-Kac Formula and Quasi-Invariance For Navier–Stokes Equations”, J. Phys. A-Math. Theor., 50:40 (2017), 405501
Kukavica I., Rusin W., Ziane M., “Localized Anisotropic Regularity Conditions For the Navier–Stokes Equations”, J. Nonlinear Sci., 27:6 (2017), 1725–1742
Barker T., Seregin G., “A Necessary Condition of Potential Blowup For the Navier–Stokes System in Half-Space”, Math. Ann., 369:3-4 (2017), 1327–1352
Kuzzay D., Saw E.-W., Martins Fabio J. W. A., Faranda D., Foucaut J.-M., Daviaud F., Dubrulle B., “New Method For Detecting Singularities in Experimental Incompressible Flows”, Nonlinearity, 30:6 (2017), 2381–2402
Zhang Z., Zhong D., Huang X., “A Refined Regularity Criterion For the Navier–Stokes Equations Involving One Non-Diagonal Entry of the Velocity Gradient”, J. Math. Anal. Appl., 453:2 (2017), 1145–1150
da Veiga H.B., “On the Extension to Slip Boundary Conditions of a Bae and Choe Regularity Criterion For the Navier–Stokes Equations. the Half-Space Case”, J. Math. Anal. Appl., 453:1 (2017), 212–220
Du L., Zhang T., “Almost Sure Existence of Global Weak Solutions For Incompressible Mud Equations in Negative-Order Sobolev Space”, J. Differ. Equ., 263:2 (2017), 1611–1642
Wang W.D., “Non Blow-Up Criterion For the 3-D Magneto-Hydrodynamics Equations in the Limiting Case”, Acta. Math. Sin.-English Ser., 33:7 (2017), 969–980
Guevara C., Nguyen Cong Phuc, “Local Energy Bounds and Epsilon-Regularity Criteria For the 3D Navier–Stokes System”, Calc. Var. Partial Differ. Equ., 56:3 (2017), 68
Ma W., Feng J., “Interior Regularity Criterion For Incompressible Ericksen-Leslie System”, Bound. Value Probl., 2017, 62
Fang D., Liu Ch., Qian Ch., “On Partial Regularity Problem For 3D Boussinesq Equations”, J. Differ. Equ., 263:7 (2017), 4156–4221
Farhat A., Grujic Z., Leitmeyer K., “The Space B-Infinity,Infinity(-1), Volumetric Sparseness, and 3D Nse”, J. Math. Fluid Mech., 19:3 (2017), 515–523
Duyckaerts T., Roy T., “Blow-Up of the Critical Sobolev Norm For Nonscattering Radial Solutions of Supercritical Wave Equations on R-3”, Bull. Soc. Math. Fr., 145:3 (2017), 503–573
Lorenz J., Zingano P.R., “Properties At Potential Blow-Up Times For the Incompressible Navier–Stokes Equations”, Bol. Soc. Parana. Mat., 35:2 (2017), 127–158
Wang F., “On Global Regularity of Incompressible Mhd Equations in R-3”, J. Math. Anal. Appl., 454:2 (2017), 936–941
J. Burczak, G. Seregin, “$LlogL$-integrability of the velocity gradient for Stokes system with drifts in $L_\infty (BMO^{-1})$”, Краевые задачи математической физики и смежные вопросы теории функций. 46, Зап. научн. сем. ПОМИ, 459, ПОМИ, СПб., 2017, 37–57
Yamazaki K., “Horizontal Biot-Savart Law in General Dimension and An Application to the 4D Magneto-Hydrodynamics”, Differ. Integral Equ., 31:3-4 (2018), 301–328
Shi Z., “Self-Similar Solutions of Stationary Navier–Stokes Equations”, J. Differ. Equ., 264:3 (2018), 1550–1580
Liu J., Wang W., “Boundary Regularity Criteria For the 6D Steady Navier–Stokes and Mhd Equations”, J. Differ. Equ., 264:3 (2018), 2351–2376
Choe H.J., Wolf J., Yang M., “A New Local Regularity Criterion For Suitable Weak Solutions of the Navier–Stokes Equations in Terms of the Velocity Gradient”, Math. Ann., 370:1-2 (2018), 629–647
Gustafson S., Roxanas D., “Global, Decaying Solutions of a Focusing Energy-Critical Heat Equation in R-4”, J. Differ. Equ., 264:9 (2018), 5894–5927
Zhang Z., “A Pointwise Regularity Criterion For Axisymmetric Navier–Stokes System”, J. Math. Anal. Appl., 461:1 (2018), 1–6
Levy G., “A Uniqueness Lemma With Applications to Regularization and Incompressible Fluid Mechanics”, Commun. Contemp. Math., 20:3 (2018), 1750048
Pooley B.C., “On a Model For the Navier–Stokes Equations Using Magnetization Variables”, J. Differ. Equ., 264:8 (2018), 5180–5196
Barker T., “Uniqueness Results For Weak Leray-Hopf Solutions of the Navier–Stokes System With Initial Values in Critical Spaces”, J. Math. Fluid Mech., 20:1 (2018), 133–160
Zhang Z., “An Improved Regularity Criterion For the Navier–Stokes Equations in Terms of One Directional Derivative of the Velocity Field”, Bull. Math. Sci., 8:1 (2018), 33–47
Duyckaerts T., Yang J., “Blow-Up of a Critical Sobolev Norm For Energy-Subcritical and Energy-Supercritical Wave Equations”, Anal. PDE, 11:4 (2018), 983–1028
Zhang Z., Li J., Yao Zh.-a., “A Remark on the Global Regularity Criterion For the 3D Navier–Stokes Equations Based on End-Point Prodi-Serrin Conditions”, Appl. Math. Lett., 83 (2018), 182–187
Jiu Q., Liu J., “Regularity Criteria to the Axisymmetric Incompressible Magneto-Hydrodynamics Equations”, Dyn. Partial Differ. Equ., 15:2 (2018), 109–126
Men Yu., Wang W., Wu G., “Endpoint Regularity Criterion For Weak Solutions of the 3D Incompressible Liquid Crystals System”, Math. Meth. Appl. Sci., 41:10 (2018), 3672–3683
Albritton D., “Blow-Up Criteria For the Navier–Stokes Equations in Non-Endpoint Critical Besov Spaces”, Anal. PDE, 11:6 (2018), 1415–1456
Liu Q., Dai G., “On the 3D Navier–Stokes Equations With Regularity in Pressure”, J. Math. Anal. Appl., 458:1 (2018), 497–507
Zhang Z., “Serrin-Type Regularity Criterion For the Navier–Stokes Equations Involving One Velocity and One Vorticity Component”, Czech. Math. J., 68:1 (2018), 219–225
Levy G., “On An Anisotropic Serrin Criterion For Weak Solutions of the Navier–Stokes Equations”, J. Math. Pures Appl., 117 (2018), 123–145
Liu Q., “Dimension of Singularities to the 3D Simplified Nematic Liquid Crystal Flows”, Nonlinear Anal.-Real World Appl., 44 (2018), 246–259
Chikami N., “On Gagliardo-Nirenberg Type Inequalities in Fourier-Herz Spaces”, J. Funct. Anal., 275:5 (2018), 1138–1172
Gibbon J.D. Gupta A. Pal N. Pandit R., “The Role of Bkm-Type Theorems in 3D Euler, Navier–Stokes and Cahn-Hilliard-Navier–Stokes Analysis”, Physica D, 376:SI (2018), 60–68
Wang W., Zhang L., Zhang Zh., “On the Interior Regularity Criteria of the 3-D Navier–Stokes Equations Involving Two Velocity Components”, Discret. Contin. Dyn. Syst., 38:5 (2018), 2609–2627
Kerr R.M., “Enstrophy and Circulation Scaling For Navier–Stokes Reconnection”, J. Fluid Mech., 839 (2018), R2
Г. А. Серёгин, Т. Н. Шилкин, “Теоремы лиувиллевского типа для уравнений Навье–Стокса”, УМН, 73:4(442) (2018), 103–170 ; G. A. Seregin, T. N. Shilkin, “Liouville-type theorems for the Navier–Stokes equations”, Russian Math. Surveys, 73:4 (2018), 661–724
Hou T.Y., Jin T., Liu P., “Potential Singularity For a Family of Models of the Axisymmetric Incompressible Flow”, J. Nonlinear Sci., 28:6, SI (2018), 2217–2247
Ye Zh., “Remark on the Regularity Criteria Via Partial Components of Vorticity to the Navier-Stokes Equations”, Math. Meth. Appl. Sci., 41:16 (2018), 6702–6716
Liu X.-g., Zhang X., “Liouville Theorem For Mhd System and Its Applications”, Commun. Pure Appl. Anal, 17:6 (2018), 2329–2350
Zhang Z., “Several New Regularity Criteria For the Axisymmetric Navier-Stokes Equations With Swirl”, Comput. Math. Appl., 76:6 (2018), 1420–1426
Li K., Ozawa T., Wang B., “Dynamical Behavior For the Solutions of the Navier-Stokes Equation”, Commun. Pure Appl. Anal, 17:4, SI (2018), 1511–1560
Liu Q., “On 3D Mhd Equations With Regularity in One Directional Derivative of the Velocity”, Comput. Math. Appl., 76:10 (2018), 2375–2383
Zhang Z., Wu Ch., “Some New Multiplicative Sobolev Inequalities With Applications to the Navier-Stokes Equations”, Ann. Pol. Math., 121:3 (2018), 279–290
Liu Q., Zhao J., “Blowup Criteria in Terms of Pressure For the 3D Nonlinear Dissipative System Modeling Electro-Diffusion”, J. Evol. Equ., 18:4 (2018), 1675–1696
Pineau B., Yu X., “A New Prodi-Serrin Type Regularity Criterion in Velocity Directions”, J. Math. Fluid Mech., 20:4 (2018), 1737–1744
Wang Ya., Wu G., Zhou D., “Some Interior Regularity Criteria Involving Two Components For Weak Solutions to the 3D Navier-Stokes Equations”, J. Math. Fluid Mech., 20:4 (2018), 2147–2159
Moffatt H.K., Kimura Y., “Towards a Finite-Time Singularity of the Navier-Stokes Equations Part 1. Derivation and Analysis of Dynamical System”, J. Fluid Mech., 861 (2018), 930–967
Yarnazaki K., “On the Navier-Stokes Equations in Scaling-Invariant Spaces in Any Dimension”, Rev. Mat. Iberoam., 34:4 (2018), 1515–1540
M. Chernobay, “On type I blow up for the Navier–Stokes equations near the boundary”, Краевые задачи математической физики и смежные вопросы теории функций. 47, К 85-летию Всеволода Алексеевича СОЛОННИКОВА, Зап. научн. сем. ПОМИ, 477, ПОМИ, СПб., 2018, 136–149
da Veiga H.B., “Navier–Stokes Equations: Some Questions Related to the Direction of the Vorticity”, Discret. Contin. Dyn. Syst.-Ser. S, 12:2, SI (2019), 203–213
Scrobogna S., “Some Remark on the Existence of Infinitely Many Nonphysical Solutions to the Incompressible Navier-Stokes Equations”, J. Math. Anal. Appl., 470:1 (2019), 226–234
Han B., Lei Zh., Li D., Zhao N., “Sharp One Component Regularity For Navier-Stokes”, Arch. Ration. Mech. Anal., 231:2 (2019), 939–970
Gibbon J.D., “Weak and Strong Solutions of the 3D Navier-Stokes Equations and Their Relation to a Chessboard of Convergent Inverse Length Scales”, J. Nonlinear Sci., 29:1 (2019), 215–228
Zhang Z., Wang W., Yang X., “An Extension and Simpler Proof of Berselli-Cordoba'S Geometric Regularity Condition For the Navier-Stokes System”, Comput. Math. Appl., 77:3 (2019), 765–769
Bradshaw Z., Farhat A., Grujic Z., “An Algebraic Reduction of the ‘`Scaling Gap’ in the Navier-Stokes Regularity Problem”, Arch. Ration. Mech. Anal., 231:3 (2019), 1983–2005
Luo X., “A Beale-Kato-Majda Criterion With Optimal Frequency and Temporal Localization”, J. Math. Fluid Mech., 21:1 (2019), UNSP 1
Buckmaster T., Vicol V., “Nonuniqueness of Weak Solutions to the Navier-Stokes Equation”, Ann. Math., 189:1 (2019), 101–144
Chen X., Juengel A., “Weak-Strong Uniqueness of Renormalized Solutions to Reaction-Cross-Diffusion Systems”, Math. Models Meth. Appl. Sci., 29:2 (2019), 237–270
Ozanski W.S., Robinson J.C., “Partial Regularity For a Surface Growth Model”, SIAM J. Math. Anal., 51:1 (2019), 228–255
Ozanski W.S., “A Sufficient Integral Condition For Local Regularity of Solutions to the Surface Growth Model”, J. Funct. Anal., 276:10 (2019), 2990–3013
Maekawa Ya., Miura H., Prange Ch., “Local Energy Weak Solutions For the Navier-Stokes Equations in the Half-Space”, Commun. Math. Phys., 367:2 (2019), 517–580
Bae H., Kang K., “Regularity Condition of the Incompressible Navier-Stokes Equations in Terms of One Velocity Component”, Appl. Math. Lett., 94 (2019), 120–125
Kukavica I., Rusin W., Ziane M., “On Local Regularity Conditions For the Navier-Stokes Equations”, Nonlinearity, 32:6 (2019), 1905–1928
Zhao J., “Regularity Criteria For the 3D Dissipative System Modeling Electro-Hydrodynamics”, Bull. Malays. Math. Sci. Soc., 42:3 (2019), 1101–1117
Albritton D., Barker T., “Global Weak Besov Solutions of the Navier-Stokes Equations and Applications”, Arch. Ration. Mech. Anal., 232:1 (2019), 197–263
Liu X.-G., Min J., Zhang X., “L-3,l-Infinity Solutions of the Liquid Crystals System”, J. Differ. Equ., 267:4 (2019), 2643–2670
Luo X., “On the Possible Time Singularities For the 3D Navier-Stokes Equations”, Physica D, 395 (2019), 37–42
Luo X., “Stationary Solutions and Nonuniqueness of Weak Solutions For the Navier-Stokes Equations in High Dimensions”, Arch. Ration. Mech. Anal., 233:2 (2019), 701–747
Liu Q., “Regularity Criterion For the 3D Micropolar Fluid Equations in Terms of Pressure”, Bull. Malays. Math. Sci. Soc., 42:4 (2019), 1305–1317
Zhang Z., Yuan W., Zhou Y., “Some Remarks on the Navier-Stokes Equations With Regularity in One Direction”, Appl. Mat., 64:3 (2019), 301–308
Xiao J., Zhang J., “N-S Systems Via Q-Q(-1) Spaces”, J. Geom. Anal., 29:2 (2019), 1490–1519
Gustafson S., Roxanas D., “Below-Threshold Solutions of a Focusing Energy-Critical Heat Equation in R-4”, Nonlinear Dispersive Waves and Fluids, Contemporary Mathematics, 725, eds. Zheng S., Beceanu M., Bona J., Chen G., VanPhan T., Soffer A., Amer Mathematical Soc, 2019, 149–162
Liu Q., “The 3D Nonlinear Dissipative System Modeling Electro-Diffusion With Blow-Up in One Direction”, Commun. Math. Sci., 17:1 (2019), 131–147

Просмотров:
Эта страница:	1135
Полный текст:	330
Литература:	93
Первая стр.:	5

Что такое QR-код?

Обратная связь:

Пользовательское соглашение

Регистрация

Логотипы