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УМН, 1999, том 54, выпуск 3(327), страницы 93–146 (Mi umn153)  

Эта публикация цитируется в 94 научных статьях (всего в 94 статьях)

Точная управляемость уравнений Навье–Стокса и Буссинеска

А. В. Фурсиковa, Ю. С. Эмануиловb

a Московский государственный университет им. М. В. Ломоносова, механико-математический факультет
b Московский государственный университет леса

DOI: https://doi.org/10.4213/rm153

Полный текст: PDF файл (534 kB)
Список литературы: PDF файл   HTML файл

Англоязычная версия:
Russian Mathematical Surveys, 1999, 54:3, 565–618

Реферативные базы данных:

УДК: 517.977.1
MSC: Primary 35Q35, 93B05; Secondary 93C20, 35B37, 76D05
Поступила в редакцию: 17.11.1998

Образец цитирования: А. В. Фурсиков, Ю. С. Эмануилов, “Точная управляемость уравнений Навье–Стокса и Буссинеска”, УМН, 54:3(327) (1999), 93–146; Russian Math. Surveys, 54:3 (1999), 565–618

Цитирование в формате AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    Эта публикация цитируется в следующих статьяx:
    1. А. В. Фурсиков, “Стабилизируемость квазилинейного параболического уравнения с помощью граничного управления с обратной связью”, Матем. сб., 192:4 (2001), 115–160  mathnet  crossref  mathscinet  zmath; A. V. Fursikov, “Stabilizability of a quasi-linear parabolic equation by means of a boundary control with feedback”, Sb. Math., 192:4 (2001), 593–639  crossref  isi
    2. Imanuvilov, OY, “Remarks on exact controllability for the Navier–Stokes equations”, ESAIM-Control Optimisation and Calculus of Variations, 6:3 (2001), 39  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    3. Coron, JM, “Local controllability of a 1-D tank containing a fluid modeled by the shallow water equations”, ESAIM-Control Optimisation and Calculus of Variations, 8 (2002), 513  crossref  mathscinet  zmath  isi  scopus  scopus
    4. Coron J.M., “Return method: Some applications to flow control”, Mathematical Control Theory, Nos 1 and 2, ICTP Lecture Notes Series, 8, 2002, 655  mathscinet  zmath  isi
    5. Fursikov A.V., “Feedback stabilization for the 2D Navier–Stokes equations”, Navier-Stokes Equations: Theory and Numerical Methods, Lecture Notes in Pure and Applied Mathematics, 223, 2002, 179–196  mathscinet  zmath  isi
    6. Barbu V., Havârneanu T., Popa C., Sritharan S.S., “Exact controllability for the magnetohydrodynamic equations”, Comm. Pure Appl. Math., 56:6 (2003), 732–783  crossref  mathscinet  zmath  isi  scopus  scopus
    7. П. О. Шорыгин, “Аппроксимативная управляемость системы Навье–Стокса в неограниченных областях”, Матем. сб., 194:11 (2003), 141–160  mathnet  crossref  mathscinet  zmath; P. O. Shorygin, “Approximate controllability of the Navier–Stokes system in unbounded domains”, Sb. Math., 194:11 (2003), 1725–1745  crossref  isi  elib
    8. А. В. Горшков, “Стабилизация полулинейного параболического уравнения, заданного во внешности ограниченной области, посредством управления с границы”, Матем. сб., 194:10 (2003), 49–76  mathnet  crossref  mathscinet  zmath; A. V. Gorshkov, “Stabilization of a semilinear parabolic equation in the exterior of a bounded domain by means of boundary controls”, Sb. Math., 194:10 (2003), 1475–1502  crossref  isi
    9. Wang Lijuan, Wang Gengsheng, “Local internal controllability of the Boussinesq system”, Nonlinear Anal., 53:5 (2003), 637–652  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    10. Agrachev A., Sarychev A., “Controllability by low modes forcing of the Navier–Stokes equation with periodic data”, 42nd IEEE Conference on Decision and Control, 1–6, 2003, 2734–2739  isi
    11. Fernández-Cara E., Guerrero S., Imanuvilov O.Yu., Puel J.-P., “Local exact controllability of the Navier–Stokes system”, J. Math. Pures Appl. (9), 83:12 (2004), 1501–1542  crossref  mathscinet  zmath  isi  scopus  scopus
    12. Gorshkov A.V., “Stabilization of linear parabolic equations defined in an exterior of a bounded domain by a boundary control”, J. Dynam. Control Systems, 10:1 (2004), 1–9  crossref  mathscinet  isi  elib  scopus  scopus
    13. Beauchard, K, “Local controllability of a 1-D Schrodinger equation”, Journal de Mathematiques Pures et Appliquees, 84:7 (2005), 851  crossref  mathscinet  zmath  isi  scopus  scopus
    14. Fursikov, AV, “Optimal boundary control for the evolutionary Navier–Stokes system: The three-dimensional case”, SIAM Journal on Control and Optimization, 43:6 (2005), 2191  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    15. Agrachev, AA, “Navier–Stokes equations: Controllability by means of low modes forcing”, Journal of Mathematical Fluid Mechanics, 7:1 (2005), 108  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus  scopus
    16. Andrey A. Agrachev, Andrey V. Sarychev, “Controllability of 2D Euler and Navier–Stokes Equations by Degenerate Forcing”, Comm Math Phys, 265:3 (2006), 673  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus  scopus
    17. A. V. Sarychev, “Lie extensions of nonlinear control systems”, Journal of Mathematical Sciences (New York), 135:4 (2006), 3195  crossref  mathscinet  zmath  elib  scopus  scopus
    18. Enrique Fernández-Cara, Sergio Guerrero, Oleg Yu. Imanuvilov, Jean-Pierre Puel, “Some Controllability Results forthe N-Dimensional Navier–Stokes and Boussinesq systems with N-1 scalar controls”, SIAM J Control Optim, 45:1 (2006), 146  crossref  mathscinet  zmath  isi  scopus  scopus
    19. Enrique Fernández-Cara, Sergio Guerrero, “Global Carleman Inequalities for Parabolic Systems and Applications to Controllability”, SIAM J Control Optim, 45:4 (2006), 1395  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    20. Sakthivel, K, “Controllability and observability theory of certain parabolic integro differential equations”, Computers & Mathematics With Applications, 52:8–9 (2006), 1299  crossref  mathscinet  zmath  isi  scopus  scopus
    21. Havarneanu, T, “Exact internal controllability for the two-dimensional Navier–Stokes equations with the Navier slip boundary conditions”, Systems & Control Letters, 55:12 (2006), 1022  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    22. Fursikov, AV, “Exact controllability and feedback stabilization from a boundary for the Navier–Stokes equations”, Control of Fluid Flow, 330 (2006), 173  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    23. Shirikyan, A, “Approximate controllability of three-dimensional Navier–Stokes equations”, Communications in Mathematical Physics, 266:1 (2006), 123  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus  scopus
    24. Barbu, V, “Tangential boundary stabilization of Navier–Stokes equations”, Memoirs of the American Mathematical Society, 181:852 (2006), 1  crossref  mathscinet  isi  elib
    25. Beauchard, K, “Controllability of a quantum particle in a moving potential well”, Journal of Functional Analysis, 232:2 (2006), 328  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    26. Guerrero, S, “Local exact controllability to the trajectories of the Boussinesq system”, Annales de l Institut Henri Poincare-Analyse Non Lineaire, 23:1 (2006), 29  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus  scopus
    27. Coron, JM, “On the small-time local controllability of a quantum particle in a moving one-dimensional infinite square potential well”, Comptes Rendus Mathematique, 342:2 (2006), 103  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    28. Fernandez-Cara, E, “Local exact controllability of micropolar fluids”, Journal of Mathematical Fluid Mechanics, 9:3 (2007), 419  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    29. Shirikyan, A, “Exact controllability in projections for three-dimensional Navier–Stokes equations”, Annales de l Institut Henri Poincare-Analyse Non Lineaire, 24:4 (2007), 521  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus  scopus
    30. Sakthivel, K, “Exact controllability of partial integrodifferential equations with mixed boundary conditions”, Journal of Mathematical Analysis and Applications, 325:2 (2007), 1257  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    31. Havarneanu T., Popa C., Sritharan S.S., “Exact Internal Controllability for the Two-Dimensional Magnetohydrodynamic Equations”, Aplimat 2007 - 6th International Conference, 2007, 169–170  mathscinet  isi
    32. Fursikov A.V., “Analyticity of stable invariant manifolds of 1D-semilinear parabolic equations”, Control Methods in PDE-Dynamical Systems, Contemporary Mathematics Series, 426, 2007, 219–242  crossref  mathscinet  zmath  isi
    33. J.-M. Coron, “Some open problems on the control of nonlinear partial differential equations”, Perspectives in Nonlinear Partial Differential Equations held in honor of Haim Brezis, Cont. Math., 446, 2007, 215–243  crossref  mathscinet  zmath  isi
    34. Karine Beauchard, “Controllablity of a quantum particle in a 1D variable domain”, ESAIM COCV, 14:1 (2008), 105  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    35. T. Tachim Medjo, R. Temam, M. Ziane, “Optimal and Robust Control of Fluid Flows: Some Theoretical and Computational Aspects”, Appl Mech Rev, 61:1 (2008), 010802  crossref  zmath  isi  scopus  scopus
    36. Sakthivel, K, “Exact controllability of nonlinear diffusion equations arising in reactor dynamics”, Nonlinear Analysis-Real World Applications, 9:5 (2008), 2029  crossref  mathscinet  zmath  isi  scopus  scopus
    37. Guerrero, S, “On the controllability of the hydrostatic Stokes equations”, Journal of Mathematical Fluid Mechanics, 10:3 (2008), 402  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    38. Beauchard, K, “Local controllability of a one-dimensional beam equation”, SIAM Journal on Control and Optimization, 47:3 (2008), 1219  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    39. Coron, JM, “Local null controllability of the two-dimensional Navier–Stokes system in the torus with a control force having a vanishing component”, Journal de Mathematiques Pures et Appliquees, 92:5 (2009), 528  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    40. González-Burgos M., Guerrero S., Puel J.-P., “Local exact controllability to the trajectories of the Boussinesq system via a fictitious control on the divergence equation”, Commun. Pure Appl. Anal., 8:1 (2009), 311–333  crossref  mathscinet  zmath  isi  scopus  scopus
    41. Tujin Kim, Daomin Cao, “Local Exact Controllability of the Navier–Stokes Equations with the Condition on the Pressure on Parts of the Boundary”, SIAM J. Control Optim., 48:6 (2010), 3805–3837  crossref  mathscinet  zmath  isi  scopus  scopus
    42. Hayk Nersisyan, “Controllability of 3D incompressible Euler equations by a finite-dimensional external force”, ESAIM COCV, 16:3 (2010), 677  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    43. А. В. Фурсиков, “Обтекание тела вязкой несжимаемой жидкостью: краевые задачи и минимизация работы жидкости”, Труды Крымской осенней математической школы-симпозиума, СМФН, 37, РУДН, М., 2010, 83–130  mathnet  mathscinet; A. V. Fursikov, “Flow of a viscous incompressible fluid around a body: boundary-value problems and minimization of the work of a fluid”, Journal of Mathematical Sciences, 180:6 (2012), 763–816  crossref
    44. Chebotarev A.Yu., “Finite-dimensional controllability for systems of Navier–Stokes type”, Differential Equations, 46:10 (2010), 1498–1506  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    45. Viorel Barbu, Sergio S. Rodrigues, Armen Shirikyan, “Internal Exponential Stabilization to a Nonstationary Solution for 3D Navier–Stokes Equations”, SIAM J. Control Optim, 49:4 (2011), 1454  crossref  mathscinet  zmath  isi  scopus  scopus
    46. Г. В. Алексеев, Д. А. Терешко, “Двухпараметрические экстремальные задачи граничного управления для стационарных уравнений тепловой конвекции”, Ж. вычисл. матем. и матем. физ., 51:9 (2011), 1645–1664  mathnet  mathscinet; G. V. Alekseev, D. A. Tereshko, “Two-parameter extremum problems of boundary control for stationary thermal convection equations”, Comput. Math. Math. Phys., 51:9 (2011), 1539–1557  crossref  isi
    47. Амосова Е.В., “Точная локальная управляемость для уравнений динамики вязкого газа”, Дифференциальные уравнения, 47:12 (2011), 1754–1754  mathscinet  zmath  isi  elib; Amosova E.V., “Exact Local Controllability for the Equations of Viscous Gas Dynamics”, Differ Equ, 47:12 (2011), 1776–1795  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    48. Nersisyan H., “Controllability of the 3D Compressible Euler System”, Comm Partial Differential Equations, 36:9 (2011), 1544–1564  crossref  mathscinet  zmath  isi  scopus  scopus
    49. Ammar-Khodja F., Benabdallah A., Gonzalez-Burgos M., de Teresa L., “Recent Results on the Controllability of Linear Coupled Parabolic Problems: a Survey”, Math. Control Relat. Fields, 1:3 (2011), 267–306  crossref  mathscinet  zmath  isi  scopus  scopus
    50. Andrei Fursikov, Alexey V. Gorshkov, “Certain questions of feedback stabilization for Navier–Stokes equations”, EECT, 1:1 (2012), 109  crossref  mathscinet  zmath  isi  scopus  scopus
    51. A. Doubova, E. Fernández-Cara, “On the control of viscoelastic Jeffreys fluids”, Systems & Control Letters, 61:4 (2012), 573  crossref  mathscinet  zmath  isi  scopus  scopus
    52. Enrique Fernández-Cara, Diego A. Souza, “On the control of some coupled systems of the Boussinesq kind with few controls”, MCRF, 2:2 (2012), 121  crossref  mathscinet  zmath  isi  scopus  scopus
    53. Sergio Guerrero, O.Yu. Imanuvilov, J.-P. Puel, “A result concerning the global approximate controllability of the Navier–Stokes system in dimension 3”, Journal de Mathématiques Pures et Appliquées, 2012  crossref  mathscinet  isi  scopus
    54. Nicolás Carreño, “Local controllability of the $N$-dimensional Boussinesq system with $N-1$ scalar controls in an arbitrary control domain”, MCRF, 2:4 (2012), 361  crossref  mathscinet  zmath  isi  scopus  scopus
    55. Burns J.A., He X., Hu W., “Control of the Boussinesq Equations with Implications for Sensor Location in Energy Efficient Buildings”, 2012 American Control Conference (Acc), Proceedings of the American Control Conference, IEEE Computer Soc, 2012, 2232–2237  crossref  mathscinet  isi
    56. Boldrini J.L., Doubova A., Fernandez-Cara E., Gonzalez-Burgos M., “Some Controllability Results for Linear Viscoelastic Fluids”, SIAM J. Control Optim., 50:2 (2012), 900–924  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    57. Hayk Nersisyan, “Stabilization of the 2D incompressible Euler system in an infinite strip”, Annales de l'Institut Henri Poincare (C) Non Linear Analysis, 2013  crossref  mathscinet  zmath  isi  scopus  scopus
    58. Florian Luca, Luz Teresa, “Control of coupled parabolic systems and Diophantine approximations”, SeMA, 2013  crossref  mathscinet
    59. Galan I.C., “Approximate Controllability of the Magnetohydrodynamic Equations on the Three-Dimensional Torus”, J. Optim. Theory Appl., 159:1 (2013), 231–245  crossref  mathscinet  zmath  isi  elib  scopus  scopus
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    62. Jean-Michel Coron, Pierre Lissy, “Local null controllability of the three-dimensional Navier–Stokes system with a distributed control having two vanishing components”, Invent. math, 2014  crossref  mathscinet  isi  scopus  scopus
    63. N.M..C. Martins, N.J..G. Carriço, H.M.. Ramos, Díd.I..C. Covas, “Velocity-distribution in pressurized pipe flow using CFD: Accuracy and mesh analysis”, Computers & Fluids, 2014  crossref  mathscinet  isi  scopus  scopus
    64. Badra M., “Local Controllability To Trajectories of the Magnetohydrodynamic Equations”, J. Math. Fluid Mech., 16:4 (2014), 631–660  crossref  mathscinet  zmath  isi  scopus  scopus
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    74. Fernandez-Cara E., Limaco J., de Menezes S.B., “Theoretical and Numerical Local Null Controllability of a Ladyzhenskaya-Smagorinsky Model of Turbulence”, 17, no. 4, 2015, 669–698  crossref  mathscinet  zmath  isi  scopus  scopus
    75. Chowdhury Sh., Mitra D., “Null Controllability of the Linearized Compressible Navier–Stokes Equations Using Moment Method”, 15, no. 2, 2015, 331–360  crossref  mathscinet  zmath  isi  scopus  scopus
    76. Shirikyan A., “Control and Mixing For 2D Navier–Stokes Equations With Space-Time Localised Noise”, 48, no. 2, 2015, 253–280  mathscinet  zmath  isi
    77. Martins N.M.C., Soares A.K., Ramos H.M., Covas D.I.C., “Cfd Modeling of Transient Flow in Pressurized Pipes”, 126, 2016, 129–140  crossref  isi  scopus  scopus
    78. Burns J.A., He X., Hu W., “Feedback stabilization of a thermal fluid system with mixed boundary control”, Comput. Math. Appl., 71:11 (2016), 2170–2191  crossref  mathscinet  isi  elib  scopus
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