Persons: Kuksin, Sergei Borisovich

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Kuksin, Sergei Borisovich

Statistics
in MathSciNet:	37 (33)
in zbMATH:	28 (25)
in Web of Science:	22 (17)
in Scopus:	13 (12)

Professor

Doctor of physico-mathematical sciences (1989)

Speciality:

01.01.03 (Mathematical physics)

Birth date:

2.03.1955

Subject:

Infinite-dimensional Hamiltonian systems, including partial differential equations of Hamiltonian form. KAM-theory. Randomly perturbed partial differential equations and statistical hydrodynamics. Turbulence in nonlinear PDEs. Elliptic equations for maps valued in compact manifolds.

https://www.mathnet.ru/eng/person19490

https://ru.wikipedia.org/wiki/Kuksin,_Sergei_Borisovich

List of publications on Google Scholar

https://zbmath.org/authors/ai:kuksin.sergei-b|kuksin.sergej-b

https://mathscinet.ams.org/mathscinet/MRAuthorID/212780

https://elibrary.ru/author_items.asp?authorid=3760

https://orcid.org/0000-0003-2322-2821

https://www.webofscience.com/wos/author/record/AAC-3293-2022

https://www.scopus.com/authid/detail.url?authorId=7003775978

List of publications:

scientific publications

by years

by types

by times cited

common list

		Citations (Crossref Cited-By Service + Math-Net.Ru)

1.	S. B. Kuksin, “Hamiltonian perturbations of infinite-dimensional linear systems with an imaginary spectrum”, Funct. Anal. Appl., 21:3 (1987), 192–205
2.	S. B. Kuksin, “Perturbation theory for quasiperiodic solutions of infinite-dimensional Hamiltonian systems, and its application to the Korteweg–de Vries equation”, Math. USSR-Sb., 64:2 (1989), 397–413
3.	S. B. Kuksin, “Perturbation of quasiperiodic solutions of infinite-dimensional Hamiltonian systems”, Math. USSR-Izv., 32:1 (1989), 39–62
4.	S. B. Kuksin, A. R. Shirikyan, “On Random Attractors for Mixing Type Systems”, Funct. Anal. Appl., 38:1 (2004), 28–37
5.	Andrey Dymov, Sergei Kuksin, “Formal expansions in stochastic model for wave turbulence 1: kinetic limit”, Comm. Math. Phys., 382 (2021), 951–1014 , arXiv: 1907.04531	15 ^[x]
6.	S. B. Kuksin, N. S. Nadirashvili, A. L. Piatnitski, “Hölder estimates for solutions of parabolic SPDEs”, Theory Probab. Appl., 47:1 (2003), 157–163
7.	R. F. Bikbaev, S. B. Kuksin, “A periodic boundary value problem for the sine-Gordon equation, its small Hamiltonian perturbations, and KAM-deformations of finite-gap tori”, St. Petersburg Math. J., 4:3 (1993), 439–468
8.	Proc. Steklov Inst. Math., 259 (2007), 128–136
9.	S. B. Kuksin, “Diffeomorphisms of function spaces corresponding to quasilinear parabolic equations”, Math. USSR-Sb., 45:3 (1983), 359–378
10.	S. B. Kuksin, “Stochastic Nonlinear Schrödinger Equation. 1. A priori Estimates”, Proc. Steklov Inst. Math., 225 (1999), 219–242
11.	S. B. Kuksin, “Reducible variational equations and the perturbation of invariant tori of Hamiltonian systems”, Math. Notes, 45:5 (1989), 373–381
12.	M. I. Vishik, S. B. Kuksin, “Perturbations of quasilinear elliptic equations and Fredholm manifolds”, Math. USSR-Sb., 58:1 (1987), 223–243
13.	Andrey Dymov, Sergey Kuksin, “Formal expansions in stochastic model for wave turbulence 2: Method of diagram decomposition”, J. Stat. Phys., 190 (2023), 3 , 61 pp., arXiv: 1907.02279	5 ^[x]
14.	A. V. Dymov, S. B. Kuksin, “On the Zakharov–Lvov stochastic model for wave turbulence”, Dokl. Math., 101:2 (2020), 102–109
15.	S. B. Kuksin, A. I. Neishtadt, “On quantum averaging, quantum KAM, and quantum diffusion”, Russian Math. Surveys, 68:2 (2013), 335–348
16.	Sergei Kuksin, “The K41 theory and turbulence in 1D Burgers equation”, Chaos, 34:2 (2024), 22103–1	3 ^[x]
17.	A. V. Bobylev, S. B. Kuksin, “Boltzmann equation and wave kinetic equations”, Keldysh Institute preprints, 2023
18.	W. Jian, S. B. Kuksin, Y. Wu, “Krylov–Bogolyubov averaging”, Russian Math. Surveys, 75:3 (2020), 427–444
19.	G. Kokarev, S. Kuksin, “Quasilinear elliptic differential equations on mappings of manifolds. I”, St. Petersburg Math. J., 15:4 (2004), 469–505
20.	S. B. Kuksin, “Conservative perturbations of infinite-dimensional linear systems depending on a vector parameter”, Funct. Anal. Appl., 23:1 (1989), 62–63
21.	Andrey Dymov, Sergei Kuksin, Alberto Maiocchi, Sergei Vlăduţ, “The Large-Period Limit for Equations of Discrete Turbulence”, Ann. Henri Poincaré, 24 (2023), 3685–3739	2 ^[x]
22.	Sergei Kuksin, “Asymptotic properties of integrals of quotients when the numerator oscillates and the denominator degenerates”, Zhurn. matem. fiz., anal., geom., 14:4 (2018), 510–518	2 ^[x]
23.	L. H. Eliasson, B. Grébert, S. B. Kuksin, “A KAM theorem for space-multidimensional Hamiltonian PDEs”, Proc. Steklov Inst. Math., 295 (2016), 129–147
24.	S. B. Kuksin, “On quasilinear parabolic equations”, Russian Math. Surveys, 35:4 (1980), 173–174
25.	T. Kappeler, V. Schroeder, S. B. Kuksin, “Poincaré inequalities for maps with target manifold of negative curvature”, Mosc. Math. J., 5:2 (2005), 399–414	1 ^[x]
26.	M. I. Vishik, S. B. Kuksin, “Quasilinear elliptic equations and Fredholm manifolds”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 1985, no. 6, 23–30
27.	S. B. Kuksin, “Conditions on the discontinuity of solutions of Prandtl–Reuss equations”, Dokl. Akad. Nauk SSSR, 279:5 (1984), 1065–1068
28.	S. B. Kuksin, “An application of monotonic semigroups in the theory of perfectly elastic plasticity”, Russian Math. Surveys, 37:5 (1982), 182–183
29.	Sergei Kuksin, Armen Shirikyan, “Mixing for dynamical systems driven by stationary noises”, Geom. Funct. Anal., 35 (2025), 1346–1399 ;
30.	Andrey V. Dymov, Sergei B. Kuksin, “On the Newton–Kantorovich Scheme for Evolutionary Equations”, Proc. Steklov Inst. Math., 327 (2024), 70–77
31.	S. B. Kuksin, A. R. Shirikyan, “Mixing in stochastic dynamical systems with stationary noise”, Russian Math. Surveys, 79:6 (2024), 1098–1100
32.	Sergei Kuksin, “Stochastic in 1d Burgers equation as a model for hydrodynamical turbulence”, Mosc. Math. J., 24:4 (2024), 603–640
33.	Russian Math. Surveys, 78:4 (2023), 585–633
34.	S. G. Vlăduţ, A. V. Dymov, S. B. Kuksin, A. Maiocchi, “A refinement of Heath-Brown's theorem on quadratic forms”, Sb. Math., 214:5 (2023), 627–675
35.	S. B. Kuksin, “Perturbation of one-gap solutions of the Korteweg–de Vries equation”, Mat. Zametki, 46:5 (1989), 96–98
36.	S. B. Kuksin, “Estimating the norm of an inverse matrix which depends on vector control”, Avtomat. i Telemekh., 1986, no. 3, 59–62
37.	A. F. Volkov, T. S. Krayukhina, S. B. Kuksin, G. B. Semenov, “Efficiency of a heuristic algorithm for allocation of periodic tasks among identical computers”, Avtomat. i Telemekh., 1985, no. 5, 148–152
38.	R. V. Goldshtejn, S. B. Kuksin, “A method of approximate solution of diffusion and heat conduction problems for domains with a large number of small defects”, Dokl. Akad. Nauk SSSR, 277:6 (1984), 1351–1354
39.	V. Ya. Rivkind, S. P. Novikov, V. M. Petkov, V. P. Myasnikov, M. V. Fedoryuk, V. V. Kucherenko, A. A. Davydov, A. I. Neishtadt, S. N. Kruzhkov, S. A. Molchanov, A. A. Ruzmaikin, D. D. Sokolov, Yu. M. Sukhov, A. G. Shukhov, B. R. Vainberg, V. I. Bakhtin, A. G. Vainshtein, B. Z. Shapiro, V. A. Kondrat'ev, O. A. Oleinik, M. I. Vishik, S. B. Kuksin, A. G. Korolev, Yu. S. Ilyashenko, “Sessions of the Petrovskii seminar on differential equations and mathemathical problems of physics”, Uspekhi Mat. Nauk, 40:5(245) (1985), 295–307
40.	R. Finn, V. I. Arnol'd, S. B. Kuksin, V. M. Kharlamov, A. V. Babin, I. G. Khachatryan, Ya. B. Zel'dovich, S. N. Samborskii, O. I. Bogoyavlenskii, “Sessions of the Petrovskii Seminar on differential equations and mathematical problems of physics”, Uspekhi Mat. Nauk, 38:2(230) (1983), 225–232
41.	S. V. Bolotin, O. È. Zubelevich, V. V. Kozlov, S. B. Kuksin, A. I. Neishtadt, “Dmitry Valerievich Treschev (on his sixtieth birthday)”, Russian Math. Surveys, 80:1 (2025), 155–160
42.	T. Bakiev, A. I. Bufetov, V. A. Vassiliev, S. M. Voronin, A. A. Glutsyuk, A. S. Gorodetski, A. V. Dukov, V. Yu. Kaloshin, A. V. Klimenko, V. V. Kozlov, S. B. Kuksin, S. K. Lando, V. S. Oganesyan, G. I. Olshanski, S. Yu. Pilyugin, O. V. Pochinka, Ya. G. Sinai, A. S. Skripchenko, A. L. Skubachevskii, I. A. Taimanov, V. A. Timorin, V. M. Tikhomirov, D. V. Treschev, D. A. Filimonov, K. M. Khanin, H. Hedenmalm, A. G. Khovanskii, M. A. Tsfasman, A. I. Shafarevich, I. S. Shilin, S. Yu. Yakovenko, “On the 80th birthday of Yulij Sergeevich Ilyashenko”, Russian Math. Surveys, 80:2 (2025), 345–357
43.	M. S. Agranovich, A. V. Babin, A. S. Demidov, Yu. A. Dubinskii, A. I. Komech, S. B. Kuksin, A. P. Kuleshov, V. P. Maslov, S. P. Novikov, V. M. Tikhomirov, A. V. Fursikov, V. V. Chepyzhov, A. I. Shnirelman, M. A. Shubin, G. I. Eskin, “Marko Iosifovich Vishik (obituary)”, Russian Math. Surveys, 68:2 (2013), 383–387
44.	C. E. Wayne, P. Gerard, W. Craig, S. B. Kuksin, A. G. Sergeev, A. V. Fursikov, “Workshop on Mathematical Hydrodynamics”, Russian Math. Surveys, 62:3 (2007), 407–408
45.	V. G. Drinfeld, A. A. Grigor'yan, Yu. S. Ilyashenko, D. Jakobson, C. E. Kenig, S. B. Kuksin, P. C. Sarnak, M. A. Tsfasman, S. G. Vlăduţ, “Nikolai Nadirashvili”, Mosc. Math. J., 5:4 (2005), 969–970
46.	M. S. Agranovich, A. V. Babin, L. R. Volevich, A. Yu. Goritskii, A. S. Demidov, Yu. A. Dubinskii, A. I. Komech, M. L. Krasnov, S. B. Kuksin, G. I. Makarenko, V. P. Maslov, V. M. Tikhomirov, A. V. Fursikov, V. V. Chepyzhov, A. I. Shnirel'man, M. A. Shubin, “Mark Iosifovich Vishik (on his 75th birthday)”, Russian Math. Surveys, 52:4 (1997), 853–861

Presentations in Math-Net.Ru

1.	Two approaches to average stochastic perturbations of integrable systems S. B. Kuksin Regular and Chaotic Dynamics. On the 30th Anniversary of the Journal Regular and Chaotic Dynamics October 27, 2025 11:10
2.	Вокруг Колмогоровского закона 4/5 и критики Львом Ландау универсальности теории турбулентности К41 S. B. Kuksin Seminar of the Department of Geometry and Topology "Geometry, Topology and Mathematical Physics", Steklov Mathematical Institute of RAS (Novikov Seminar) November 19, 2024 16:45
3.	Long-time behaviour of trajectories for dynamical systems with random forces: non-Markov case S. B. Kuksin Dynamics days in Sirius. On the occasion of academician Dmitry V. Treschev’s anniversary October 31, 2024 09:30
4.	Dynamical systems with random forces at long times : an introduction to theory S. B. Kuksin October 3, 2024 17:00
5.	Random perturbations of integrable systems with applications to noisy oscillator chains S. B. Kuksin Dobrushin Mathematics Laboratory Seminar March 19, 2024 16:00
6.	Строгие результаты для стохастической модели волновой турбулентности Захарова–Львова A. V. Dymov, S. B. Kuksin Annual Session of Steklov Mathematical Institute (Best results 2023) November 15, 2023 16:20
7.	Случайные возмущения линейных и интегрируемых Гамильтоновых систем S. B. Kuksin Traditional session of MIAN-PDMI "Differential Equations and Dynamical Systems" May 14, 2023 10:45
8.	Lecture 10. Random dynamical systems A. V. Dymov, S. B. Kuksin Course by A. V. Dymov and S. B. Kuksin "Random dynamical systems" April 28, 2023 18:00
9.	Теория турбулентности А. Н. Колмогорова, ее развитие, критика и строгая одномерная модель S. B. Kuksin Conference "Kolmogorov-120. MIAN" April 26, 2023 16:00
10.	Lecture 9. Random dynamical systems A. V. Dymov, S. B. Kuksin Course by A. V. Dymov and S. B. Kuksin "Random dynamical systems" April 21, 2023 18:00
11.	Lecture 8. Random dynamical systems A. V. Dymov, S. B. Kuksin Course by A. V. Dymov and S. B. Kuksin "Random dynamical systems" April 14, 2023 18:00
12.	Lecture 7. Random dynamical systems A. V. Dymov, S. B. Kuksin Course by A. V. Dymov and S. B. Kuksin "Random dynamical systems" April 7, 2023 18:00
13.	Lecture 5. Random dynamical systems A. V. Dymov, S. B. Kuksin Course by A. V. Dymov and S. B. Kuksin "Random dynamical systems" March 24, 2023 18:00
14.	Lecture 4. Random dynamical systems S. B. Kuksin Course by A. V. Dymov and S. B. Kuksin "Random dynamical systems" March 17, 2023 18:00
15.	Lecture 3. Random dynamical systems A. V. Dymov, S. B. Kuksin Course by A. V. Dymov and S. B. Kuksin "Random dynamical systems" March 10, 2023 18:00
16.	Kolmogorov's theory of turbulence, the Landau criticism and their rigorous 1d versions S. B. Kuksin Beijing–Moscow Mathematics Colloquium March 10, 2023 12:00
17.	Lecture 2. Random dynamical systems A. V. Dymov, S. B. Kuksin Course by A. V. Dymov and S. B. Kuksin "Random dynamical systems" March 3, 2023 18:00
18.	Lecture 1. Random dynamical systems A. V. Dymov, S. B. Kuksin Course by A. V. Dymov and S. B. Kuksin "Random dynamical systems" February 17, 2023 18:00
19.	K41 and burgulence S. B. Kuksin Steklov Mathematical Institute Seminar December 15, 2022 16:00
20.	On rigorous one-dimensional versions of two heuristic laws of Kolmogorov's theory of turbulence S. B. Kuksin Scientific seminar on the differential and functional differential equations November 8, 2022 12:00
21.	On the 2/3- and 4/5-laws of the Kolmogorov theory of turbulence and their rigorous 1d versions S. B. Kuksin International Conference "New Trends in Mathematical Physics" November 7, 2022 14:30
22.	Уравнение Бюргерса как удивительная модель теории турбулентности Колмогорова S. B. Kuksin Hamiltonian systems and statistical mechanics October 17, 2022 16:30
23.	Теория турбулентности А.Н. Колмогорова и ее строгая одномерная модель. Лекция 2 S. B. Kuksin Scientific seminar on the differential and functional differential equations May 26, 2022 15:00
24.	Теория турбулентности Колмогорова К41 и ее строгая одномерная модель S. B. Kuksin Seminar of the Department of Geometry and Topology "Geometry, Topology and Mathematical Physics", Steklov Mathematical Institute of RAS (Novikov Seminar) May 25, 2022 14:00
25.	Усреднение для случайно возмущенных интегрируемых систем S. B. Kuksin Hamiltonian systems and statistical mechanics May 23, 2022
26.	Теория турбулентности А.Н. Колмогорова и ее строгая одномерная модель. Лекция 1 S. B. Kuksin Scientific seminar on the differential and functional differential equations May 19, 2022 15:00
27.	Two models for wave turbulence S. B. Kuksin Dynamical Systems and PDEs February 16, 2022 18:00
28.	Заседание, посвященное 100-летию со дня рождения Марка Иосифовича Вишика A. V. Fursikov, A. S. Demidov, S. B. Kuksin, V. V. Chepyzhov, V. M. Tikhomirov, Yu. A. Dubinskii, A. L. Skubachevskii, V. B. Demidovich Meetings of the Moscow Mathematical Society November 9, 2021 18:30
29.	Long-time behaviour of solutions for nonlinear PDEs with bounded random forces S. B. Kuksin Mathematical Physics, Dynamical Systems and Infinite-Dimensional Analysis – 2021 July 5, 2021 18:00
30.	Мини-конференция, посвящённая 75-летию Александра Ильича Комеча A. A. Ilyin, S. B. Kuksin, A. I. Shnirel'man Dobrushin Mathematics Laboratory Seminar May 25, 2021 16:00
31.	Kolmogorov theory of turbulence and its rigorous model, given by the Burgers equation S. B. Kuksin Dynamical Systems and PDEs September 30, 2020 17:00
32.	Rigorous theory of 1d turbulence S. B. Kuksin International Conference "Classical Mechanics, Dynamical Systems and Mathematical Physics" on the occasion of V. V. Kozlov 70th birthday January 20, 2020 15:45
33.	Ergodicity, mixing and KAM Sergei Kuksin International conference «Real and Complex Dynamical Systems», dedicated to the to the 75th anniversary of Yu. S. Il'yashenko November 30, 2018 11:55
34.	Controllability, mixing and the Nash-Moser scheme for SPDEs S. B. Kuksin Dobrushin Mathematics Laboratory Seminar May 23, 2017 16:00
35.	Small-amplitude solutions for space-multidimensional hamiltonian PDEs under periodic boundary conditions S. B. Kuksin Dobrushin Mathematics Laboratory Seminar July 12, 2016 16:00
36.	Малоамплитудные решения многомерных волновых уравнений S. B. Kuksin Seminar of the Department of Mathematical Physics, Steklov Mathematical Institute of RAS October 22, 2015 11:00
37.	KAM theory and the 3d Euler equation S. B. Kuksin International scientific conference "Days of Classical Mechanics" January 26, 2015 10:05
38.	Small oscillations in space-multidimensional Hamiltonian PDE S. B. Kuksin The Seventh International Conference on Differential and Functional Differential Equations August 28, 2014 10:00
39.	KAM-theory for PDE with one and many space variables S. B. Kuksin International conference "Analysis and Singularities" dedicated to the 75th anniversary of Vladimir Igorevich Arnold December 17, 2012 15:40
40.	What is interesting in differential equations with random force? S. B. Kuksin Globus Seminar August 30, 2012 15:40
41.	Hydrodynamics and turbulence S. B. Kuksin Summer School "Contemporary Mathematics", 2010 July 26, 2010 12:45
42.	Speech at the General meeting of Steklov members dedicated to 75th anniversary of Steklov Mathematical Institute S. B. Kuksin General meeting of Steklov members dedicated to 75th anniversary of Steklov Mathematical Institute June 5, 2009 17:30
43.	Dissipative perturbations of integrable PDE S. B. Kuksin International Conference of Steklov Institute Members, working outside Russia June 5, 2009 12:30
44.	Three theorems on perturbed KdV equation on a circle S. B. Kuksin International conference "Analysis and Singularities" dedicated to 70th anniversary of Vladimir Igorevich Arnold August 24, 2007 09:00

Organisations