## Kuksin, Sergeĭ B.

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 Author ID: kuksin.sergei-b Published as: Kuksin, S. B.; Kuksin, Sergei; Kuksin, Sergei B.; Kuksin, Sergej B.; Kuksin, S.; Kuksin, Sergeĭ B.; Kuksin, Sergeï B.; Kuksin, Sergej more...less Homepage: https://webusers.imj-prg.fr/~sergei.kuksin/ External Links: MGP · Wikidata · Math-Net.Ru · GND · IdRef · theses.fr
 Documents Indexed: 138 Publications since 1978, including 5 Books 2 Contributions as Editor Biographic References: 1 Publication Co-Authors: 68 Co-Authors with 69 Joint Publications 2,605 Co-Co-Authors
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### Co-Authors

 71 single-authored 13 Shirikyan, Armen R. 7 Eliasson, L. Hakan 4 Maiocchi, Alberto Mario 3 Bikbaev, Ramil’ F. 3 Dymov, Andrey V. 3 Kappeler, Thomas 3 Nersesyan, Vahagn 3 Piatnitski, Andrey L. 3 Pöschel, Jürgen 3 Vishik, Marko Iosifovich 2 Agranovich, Mikhail Semënovich 2 Babin, Anatoli V. 2 Bambusi, Dario 2 Bobenko, Alexander Ivanovich 2 Chepyzhov, Vladimir V. 2 Chueshov, Igor’ Dmitrievich 2 Demidov, Alexandre Sergeevich 2 Dubinskiĭ, Yuliĭ Andreevich 2 Fursikov, Andreĭ Vladimirovich 2 Grébert, Benoît 2 Huang, Guan 2 Khesin, Boris A. 2 Kokarev, Gerasim 2 Komech, Alexander Ilich 2 Maslov, Viktor Pavlovich 2 Nadirashvili, Nikolai S. 2 Peralta-Salas, Daniel 2 Perelman, Galina 2 Schröder, Viktor M. H. 2 Shnirelman, Alexander I. 2 Shubin, Mikhail Aleksandrovich 2 Tikhomirov, Vladimir Mikhaĭlovich 1 Agrachev, Andreĭ Aleksandrovich 1 Bardos, Claude Williams 1 Boritchev, Alexandre 1 Brandenberger, Robert H. 1 Drinfeld, Vladimir Gershonovich 1 Eskin, Gregory 1 Gol’dshtejn, R. V. 1 Goritskiĭ, Andreĭ Yur’evich 1 Grigor’yan, Alexander Asaturovich 1 Guan, Huang 1 Guyenne, Philippe 1 Ilyashenko, Yulij Sergeevich 1 Jakobson, Dmitry 1 Jian, Wenwen 1 Kelaï, Takfarinas 1 Kenig, Carlos Eduardo 1 Korotyaev, Evgeny L. 1 Krasnov, M. L. 1 Kuleshov, A. P. 1 Lazutkin, Vladimir Fedorovich 1 Makarenko, G. I. 1 Mischaikow, Konstantin 1 Neĭshtadt, Anatoliĭ Iserovich 1 Novikov, Sergeĭ Petrovich 1 Pelinovsky, Dmitry Efimovich 1 Penrose, Oliver 1 Sarnak, Peter Clive 1 Saut, Jean-Claude 1 Sulem, Catherine 1 Tsfasman, Michael A. 1 Vlǎduţ, Sergei Georgievich 1 Volevich, Leonid Romanovich 1 Wayne, Clarence Eugene 1 Wu, Yuan 1 Yi, Yingfei 1 Zhang, Huilin
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### Serials

 8 Communications in Mathematical Physics 7 Geometric and Functional Analysis. GAFA 6 Russian Mathematical Surveys 4 Journal of Statistical Physics 4 Moscow University Mathematics Bulletin 4 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 4 Vestnik Moskovskogo Universiteta. Seriya I. Matematika, Mekhanika 4 Séminaire Laurent Schwartz. EDP et Applications 3 Journal of Applied Mathematics and Mechanics 3 Functional Analysis and its Applications 3 Physica D 3 Mathematics of the USSR, Sbornik 2 Archive for Rational Mechanics and Analysis 2 Matematicheskie Zametki 2 Nonlinearity 2 Uspekhi Matematicheskikh Nauk [N. S.] 2 ZAMP. Zeitschrift für angewandte Mathematik und Physik 2 Matematicheskiĭ Sbornik. Novaya Seriya 2 Journal de Mathématiques Pures et Appliquées. Neuvième Série 2 Soviet Physics. Doklady 2 Annales de l’Institut Henri Poincaré. Probabilités et Statistiques 2 Russian Journal of Mathematical Physics 2 Séminaire Équations aux Dérivées Partielles 2 St. Petersburg Mathematical Journal 2 Annals of Mathematics. Second Series 2 Moscow Mathematical Journal 2 Proceedings of the Steklov Institute of Mathematics 2 Stochastic and Partial Differential Equations. Analysis and Computations 1 Communications on Pure and Applied Mathematics 1 Letters in Mathematical Physics 1 Mathematical Notes 1 Reviews in Mathematical Physics 1 Chaos, Solitons and Fractals 1 Theory of Probability and its Applications 1 Advances in Mathematics 1 Commentarii Mathematici Helvetici 1 Funktsional’nyĭ Analiz i ego Prilozheniya 1 Mathematics of the USSR. Izvestiya 1 Ergodic Theory and Dynamical Systems 1 Annals of Global Analysis and Geometry 1 Algebra i Analiz 1 Differential Geometry and its Applications 1 Automation and Remote Control 1 Izvestiya Akademii Nauk SSSR. Seriya Matematicheskaya 1 Journal of Physics A: Mathematical and General 1 Stochastic Processes and their Applications 1 Notices of the American Mathematical Society 1 Journal of Dynamics and Differential Equations 1 Journal of Nonlinear Science 1 Bulletin des Sciences Mathématiques 1 Discrete and Continuous Dynamical Systems 1 Documenta Mathematica 1 Doklady Mathematics 1 Mathematical Physics, Analysis and Geometry 1 Reviews in Mathematics and Mathematical Physics 1 Journal of Dynamical and Control Systems 1 Communications in Contemporary Mathematics 1 Journal of Mathematical Physics, Analysis, Geometry 1 Cambridge Tracts in Mathematics 1 Lecture Notes in Mathematics 1 Mathematical Surveys and Monographs 1 Oxford Lecture Series in Mathematics and its Applications 1 Annales Mathématiques du Québec 1 Journal de l’École Polytechnique – Mathématiques 1 Progress in Nonlinear Differential Equations and Their Applications 1 Zurich Lectures in Advanced Mathematics
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### Fields

 100 Partial differential equations (35-XX) 58 Dynamical systems and ergodic theory (37-XX) 24 Probability theory and stochastic processes (60-XX) 24 Fluid mechanics (76-XX) 11 Mechanics of deformable solids (74-XX) 7 Ordinary differential equations (34-XX) 7 Global analysis, analysis on manifolds (58-XX) 6 Functional analysis (46-XX) 6 Differential geometry (53-XX) 5 Operator theory (47-XX) 5 Systems theory; control (93-XX) 4 History and biography (01-XX) 4 Mechanics of particles and systems (70-XX) 3 Quantum theory (81-XX) 2 General and overarching topics; collections (00-XX) 2 Linear and multilinear algebra; matrix theory (15-XX) 2 Group theory and generalizations (20-XX) 2 Numerical analysis (65-XX) 1 Real functions (26-XX) 1 Measure and integration (28-XX) 1 Difference and functional equations (39-XX) 1 Approximations and expansions (41-XX) 1 Integral equations (45-XX) 1 Algebraic topology (55-XX) 1 Classical thermodynamics, heat transfer (80-XX) 1 Statistical mechanics, structure of matter (82-XX) 1 Geophysics (86-XX)

### Citations contained in zbMATH Open

104 Publications have been cited 1,856 times in 834 Documents Cited by Year
Nearly integrable infinite-dimensional Hamiltonian systems. Zbl 0784.58028
Kuksin, Sergej B.
1993
Invariant Cantor manifolds of quasi-periodic oscillations for a nonlinear Schrödinger equation. Zbl 0847.35130
Kuksin, Sergej; Pöschel, Jürgen
1996
KAM for the nonlinear Schrödinger equation. Zbl 1201.35177
Eliasson, L. Hakan; Kuksin, Sergei B.
2010
Mathematics of two-dimensional turbulence. Zbl 1333.76003
Kuksin, Sergei; Shirikyan, Armen
2012
Analysis of Hamiltonian PDE’s. Zbl 0960.35001
Kuksin, S. B.
2000
On reducibility of Schrödinger equations with quasiperiodic in time potentials. Zbl 1176.35141
Eliasson, Håkan L.; Kuksin, Sergei B.
2009
Hamiltonian perturbations of infinite-dimensional linear systems with an imaginary spectrum. Zbl 0716.34083
Kuksin, S. B.
1987
Hamiltonian perturbations of infinite-dimensional linear systems with imaginary spectrum. Zbl 0631.34069
Kuksin, S. B.
1987
KAM for the nonlinear beam equation. Zbl 1370.35214
Eliasson, L. Hakan; Grébert, Benoît; Kuksin, Sergei B.
2016
A KAM-theorem for equations of the Korteweg-de Vries type. Zbl 0920.35135
Kuksin, S. B.
1998
Stochastic dissipative PDE’s and Gibbs measures. Zbl 0974.60046
Kuksin, Sergei; Shirikyan, Armen
2000
A coupling approach to randomly forced nonlinear PDE’s. I. Zbl 0991.60056
Kuksin, Sergei; Shirikyan, Armen
2001
Coupling approach to white-forced nonlinear PDEs. Zbl 1021.37044
Kuksin, Sergei; Shirikyan, Armen
2002
The Eulerian limit for 2D statistical hydrodynamics. Zbl 1157.76319
Kuksin, Sergei B.
2004
Ergodicity for the randomly forced 2D Navier-Stokes equations. Zbl 1013.37046
Kuksin, Sergei; Shirikyan, Armen
2001
On small-denominators equations with large variable coefficients. Zbl 0886.35044
Kuksin, Sergej B.
1997
Randomly forced CGL equation: stationary measures and the inviscid limit. Zbl 1047.35061
Kuksin, Sergei; Shirikyan, Armen
2004
Perturbation of quasiperiodic solutions of infinite-dimensional Hamiltonian systems. Zbl 0667.58060
Kuksin, S. B.
1989
Khasminskii-Whitham averaging for randomly perturbed KdV equation. Zbl 1148.35077
Kuksin, Sergei B.; Piatnitski, Andrey L.
2008
Vey theorem in infinite dimensions and its application to KdV. Zbl 1193.37076
Kuksin, Sergei; Perelman, Galina
2010
Infinite-dimensional symplectic capacities and a squeezing theorem for Hamiltonian PDE’s. Zbl 0827.35121
Kuksin, Sergej B.
1995
Random kick-forced 3D Navier-Stokes equations in a thin domain. Zbl 1133.76015
Chueshov, Igor; Kuksin, Sergei
2008
Oscillation in space-periodic nonlinear Schrödinger equations. Zbl 0874.35113
Kuksin, S. B.
1997
On the inclusion of analytic symplectic maps in analytic Hamiltonian flows and its applications. Zbl 0797.58025
Kuksin, Sergei; Pöschel, Jürgen
1994
Stochastic 3D Navier-Stokes equations in a thin domain and its $$\alpha$$-approximation. Zbl 1143.76422
Chueshov, Igor; Kuksin, Sergei
2008
Randomly forced nonlinear PDEs and statistical hydrodynamics in 2 space dimensions. Zbl 1099.35083
Kuksin, Sergei B.
2006
Spectral properties of solutions for nonlinear PDEs in the turbulent regime. Zbl 0929.35145
Kuksin, S. B.
1999
On finite-dimensional projections of distributions for solutions of randomly forced 2D Navier-Stokes equations. Zbl 1177.60059
Agrachev, A.; Kuksin, S.; Sarychev, A.; Shirikyan, A.
2007
Damped-driven KdV and effective equations for long-time behaviour of its solutions. Zbl 1231.35205
Kuksin, Sergei B.
2010
Exponential mixing for a class of dissipative PDEs with bounded degenerate noise. Zbl 1442.35437
Kuksin, Sergei; Nersesyan, Vahagn; Shirikyan, Armen
2020
The nonlinear Klein-Gordon equation on an interval as a perturbed sine-Gordon equation. Zbl 0842.35099
Bobenko, Alexander I.; Kuksin, Sergej B.
1995
Fifteen years of KAM for PDE. Zbl 1067.37110
Kuksin, Sergei B.
2004
A coupling approach to randomly forced nonlinear PDE’s. II. Zbl 1010.60066
Kuksin, Sergei; Piatniski, Andrey; Shirikyan, Armen
2002
Four lectures on KAM for the nonlinear Schrödinger equation. Zbl 1140.37021
Eliasson, L. H.; Kuksin, S. B.
2008
The KdV equation under periodic boundary conditions and its perturbations. Zbl 1301.35132
Guan, Huang; Kuksin, Sergei
2014
KAM theory and the 3D Euler equation. Zbl 1303.37035
Khesin, Boris; Kuksin, Sergei; Peralta-Salas, Daniel
2014
On the parametrization of finite-gap solutions by frequency and wavenumber vectors and a theorem of I. Krichever. Zbl 0774.35070
Bikbaev, Ramil F.; Kuksin, Sergej B.
1993
Perturbation of conditionally periodic solutions of infinite-dimensional Hamiltonian systems. Zbl 0662.58036
Kuksin, S. B.
1988
Perturbation theory for quasiperiodic solutions of infinite-dimensional Hamiltonian systems, and its applications to the Korteweg-de Vries equation. Zbl 0678.58037
Kuksin, S. B.
1989
On turbulence in nonlinear Schrödinger equations. Zbl 0912.35143
Kuksin, S. B.
1997
On random attractors for mixing type systems. Zbl 1086.37027
Kuksin, S. B.; Shirikyan, A.
2004
Infinite Toeplitz-Lipschitz matrices and operators. Zbl 1140.15025
Eliasson, H. L.; Kuksin, S. B.
2008
On distribution of energy and vorticity for solutions of 2D Navier-Stokes equation with small viscosity. Zbl 1168.35034
Kuksin, Sergei B.
2008
Hölder estimates for solutions of parabolic SPDEs. Zbl 1038.60058
Kuksin, S. B.; Nadirashvili, N. S.; Pyatnitskij, A. L.
2002
Weakly nonlinear stochastic CGL equations. Zbl 1280.35144
Kuksin, Sergei B.
2013
Perturbation theory of conditionally periodic solutions of infinite- dimensional Hamiltonian systems and its application to the Korteweg-de Vries equation. Zbl 0657.58033
Kuksin, S. B.
1988
On squeezing and flow of energy for nonlinear wave equations. Zbl 0834.35086
Kuksin, S. B.
1995
Stochastic CGL equations without linear dispersion in any space dimension. Zbl 1287.60093
Kuksin, Sergei; Nersesyan, Vahagn
2013
Growth and oscillations of solutions of nonlinear Schrödinger equation. Zbl 0862.35112
Kuksin, Sergei B.
1996
Derivation of a wave kinetic equation from the resonant-averaged stochastic NLS equation. Zbl 1364.35336
Kuksin, Sergei; Maiocchi, Alberto
2015
Elements of a qualitative theory of Hamiltonian PDEs. Zbl 0967.35123
Kuksin, Sergei B.
1998
A periodic boundary value problem for the sine-Gordon equation, its small Hamiltonian perturbations and KAM deformations of finite-zone tori. Zbl 0771.35052
Bikbaev, R. F.; Kuksin, S. B.
1992
Eulerian limit for 2D Navier-Stokes equation and damped/driven KdV equation as its model. Zbl 1161.35461
Kuksin, S. B.
2007
On the inclusion of an almost integrable analytic symplectomorphism into a Hamiltonian flow. Zbl 0931.37030
Kuksin, Sergei B.
1993
Stochastic nonlinear Schrödinger equation. I: A priori estimates. Zbl 0984.60070
Kuksin, S. B.
1999
Mixing via controllability for randomly forced nonlinear dissipative PDEs. (Mélange via la contrôlabilité pour des EDP non linéaires dissipatives bruitées.) Zbl 1451.35071
Kuksin, Sergei; Nersesyan, Vahagn; Shirikyan, Armen
2020
Diffeomorphisms of functional spaces corresponding to quasilinear parabolic equations. Zbl 0501.35046
Kuksin, S. B.
1982
Asymptotic expansions for some integrals of quotients with degenerated divisors. Zbl 1382.28005
Kuksin, Sergei
2017
Perturbations of the harmonic map equation. Zbl 1063.58012
Kappeler, T.; Kuksin, S.; Schroeder, V.
2003
Some limiting properties of randomly forced two-dimensional Navier-Stokes equations. Zbl 1060.35106
Kuksin, Sergei; Shirikyan, Armen
2003
KAM-theory for partial differential equations. Zbl 0821.35130
Kuksin, S. B.
1994
Time-averaging for weakly nonlinear CGL equations with arbitrary potentials. Zbl 1331.35331
Huang, Guan; Kuksin, Sergei; Maiocchi, Alberto
2015
Ergodic theorems for 2D statistical hydrodynamics. Zbl 1030.37054
Kuksin, Sergei B.
2002
A family of balance relations for the two-dimensional Navier-Stokes equations with random forcing. Zbl 1064.76027
Kuksin, Sergei; Penrose, Oliver
2005
Resonant averaging for small-amplitude solutions of stochastic nonlinear Schrödinger equations. Zbl 1391.35437
Kuksin, Sergei; Maiocchi, Alberto
2018
Exponential mixing for dissipative PDEs with bounded non-degenerate noise. Zbl 1440.35272
Kuksin, Sergei; Zhang, Huilin
2020
A periodic boundary value problem for the sine-Gordon equation, small Hamiltonian perturbations of it, and KAM-deformations of finite-gap tori. Zbl 0791.35118
Bikbaev, R. F.; Kuksin, S. B.
1992
An infinitesimal Liouville-Arnold theorem as a criterion of reducibility for variational Hamiltonian equations. Zbl 0769.58022
Kuksin, Sergej B.
1992
Global, local and dense non-mixing of the 3D Euler equation. Zbl 1451.35122
Khesin, Boris; Kuksin, Sergei; Peralta-Salas, Daniel
2020
Remarks on the balance relations for the two-dimensional Navier-Stokes equation with random forcing. Zbl 1089.76013
Kuksin, Sergei B.
2006
An application of monotone semigroups in the theory of perfect elastoplasticity. Zbl 0513.73039
Kuksin, S. B.
1982
Quasilinear elliptic equations and Fredholm manifolds. Zbl 0599.35041
Vishik, M. I.; Kuksin, S. B.
1985
Quasi-linear elliptic differential equations for mappings of manifolds. II. Zbl 1232.58005
Kokarev, Gerasim; Kuksin, Sergei
2007
Strong nonresonance of Schrödinger operators and an averaging theorem. Zbl 0885.35119
Kappeler, T.; Kuksin, S.
1995
Hamiltonian PDEs. (With an appendix by Dario Bambusi). Zbl 1130.37392
Kuksin, Sergei B.
2006
On exponential convergence to a stationary measure for nonlinear PDEs perturbed by random kick-forces, and the turbulence limit. Zbl 1023.37031
Kuksin, Sergei B.
2002
The limit of small Rossby numbers for randomly forced quasi-geostrophic equation on $$\beta$$-plane. Zbl 1327.35462
Kuksin, Sergei; Maiocchi, Alberto
2015
One-dimensional turbulence and the stochastic Burgers equation. Zbl 1486.60002
Boritchev, Alexandre; Kuksin, Sergei
2021
Conditions on a discontinuity of solutions of the Prandtl-Reuss equations. Zbl 0584.73040
Kuksin, S. B.
1984
Perturbations of quasilinear elliptic equations and Fredholm manifolds. Zbl 0625.35029
Vishik, M. I.; Kuksin, S. B.
1987
Reducible equations in variations and perturbations of invariant tori of Hamiltonian systems. Zbl 0684.58013
Kuksin, S. B.
1989
Double-periodic solutions of nonlinear Cauchy-Riemann equations. Zbl 0855.58048
Kuksin, Sergej B.
1996
Asymptotic properties of integrals of quotients when the numerator oscillates and the denominator degenerates. Zbl 07116939
Kuksin, Sergei
2018
KdV Hamiltonian as a function of actions. Zbl 1351.37243
Korotyaev, Evgeny L.; Kuksin, Sergei
2016
Rigorous results and conjectures on stationary space-periodic 2D turbulence. Zbl 1171.35445
Kuksin, Sergei B.
2007
An averaging theorem for distributed conservative systems and its application to von Kármán’s equations. Zbl 0722.73039
Kuksin, S. B.
1989
On quantum averaging, quantum KAM, and quantum diffusion. Zbl 1271.81066
Kuksin, S. B.; Neishtadt, A. I.
2013
Analyticity of solutions for quasilinear wave equations and other quasilinear systems. Zbl 1330.35261
2014
Poincaré inequalities for maps with target manifold of negative curvature. Zbl 1093.53037
Kappeler, T.; Schroeder, V.; Kuksin, S.
2005
Formal expansions in stochastic model for wave turbulence. I: Kinetic limit. Zbl 1482.35211
Dymov, Andrey; Kuksin, Sergei
2021
Analytic dependence of the solutions of some monotone parabolic equations on the initial conditions. Zbl 0389.35040
Kuksin, S. B.
1978
Introduction to the stochastic Burgers equation and Burgulence. (Introduction à l’équation de Burgers stochastique et à la Burgulence.) Zbl 1401.35358
Kelaï, Takfarinas; Kuksin, Sergei
2016
The control problem for the process of elasto-plastic deformation. Zbl 0596.73016
Kuksin, S. B.
1983
Generalized solutions of the dynamic problem of perfect elastoplasticity. Zbl 0604.73027
Kuksin, S. B.
1985
Conservative perturbations of infinite-dimensional linear systems depending on a vector parameter. Zbl 0688.58033
Kuksin, S. B.
1989
On the character of dependence of the solutions to nonlinear parabolic equations on initial conditions. Zbl 0433.35033
Kuksin, S. B.
1979
On quasilinear parabolic equations. Zbl 0448.35052
Kuksin, S. B.
1980
On quasilinear parabolic equations. Zbl 0466.35045
Kuksin, S. B.
1980
Small-amplitude solutions of the sine-Gordon equation on an interval under Dirichlet or Neumann boundary conditions. Zbl 0839.35117
Bobenko, A. I.; Kuksin, S. B.
1995
Lectures on Hamiltonian methods in nonlinear PDEs. Zbl 1123.37028
Kuksin, Sergei
2005
One-dimensional turbulence and the stochastic Burgers equation. Zbl 1486.60002
Boritchev, Alexandre; Kuksin, Sergei
2021
Formal expansions in stochastic model for wave turbulence. I: Kinetic limit. Zbl 1482.35211
Dymov, Andrey; Kuksin, Sergei
2021
On the energy transfer to high frequencies in the damped/driven nonlinear Schrödinger equation. Zbl 1478.35192
Huang, Guan; Kuksin, Sergei
2021
Exponential mixing for a class of dissipative PDEs with bounded degenerate noise. Zbl 1442.35437
Kuksin, Sergei; Nersesyan, Vahagn; Shirikyan, Armen
2020
Mixing via controllability for randomly forced nonlinear dissipative PDEs. (Mélange via la contrôlabilité pour des EDP non linéaires dissipatives bruitées.) Zbl 1451.35071
Kuksin, Sergei; Nersesyan, Vahagn; Shirikyan, Armen
2020
Exponential mixing for dissipative PDEs with bounded non-degenerate noise. Zbl 1440.35272
Kuksin, Sergei; Zhang, Huilin
2020
Global, local and dense non-mixing of the 3D Euler equation. Zbl 1451.35122
Khesin, Boris; Kuksin, Sergei; Peralta-Salas, Daniel
2020
On the Zakharov-L’vov stochastic model for wave turbulence. Zbl 1479.35783
Dymov, A. V.; Kuksin, S. B.
2020
Resonant averaging for small-amplitude solutions of stochastic nonlinear Schrödinger equations. Zbl 1391.35437
Kuksin, Sergei; Maiocchi, Alberto
2018
Asymptotic properties of integrals of quotients when the numerator oscillates and the denominator degenerates. Zbl 07116939
Kuksin, Sergei
2018
Asymptotic expansions for some integrals of quotients with degenerated divisors. Zbl 1382.28005
Kuksin, Sergei
2017
KAM for the nonlinear beam equation. Zbl 1370.35214
Eliasson, L. Hakan; Grébert, Benoît; Kuksin, Sergei B.
2016
KdV Hamiltonian as a function of actions. Zbl 1351.37243
Korotyaev, Evgeny L.; Kuksin, Sergei
2016
Introduction to the stochastic Burgers equation and Burgulence. (Introduction à l’équation de Burgers stochastique et à la Burgulence.) Zbl 1401.35358
Kelaï, Takfarinas; Kuksin, Sergei
2016
Derivation of a wave kinetic equation from the resonant-averaged stochastic NLS equation. Zbl 1364.35336
Kuksin, Sergei; Maiocchi, Alberto
2015
Time-averaging for weakly nonlinear CGL equations with arbitrary potentials. Zbl 1331.35331
Huang, Guan; Kuksin, Sergei; Maiocchi, Alberto
2015
The limit of small Rossby numbers for randomly forced quasi-geostrophic equation on $$\beta$$-plane. Zbl 1327.35462
Kuksin, Sergei; Maiocchi, Alberto
2015
The KdV equation under periodic boundary conditions and its perturbations. Zbl 1301.35132
Guan, Huang; Kuksin, Sergei
2014
KAM theory and the 3D Euler equation. Zbl 1303.37035
Khesin, Boris; Kuksin, Sergei; Peralta-Salas, Daniel
2014
Analyticity of solutions for quasilinear wave equations and other quasilinear systems. Zbl 1330.35261
2014
Weakly nonlinear stochastic CGL equations. Zbl 1280.35144
Kuksin, Sergei B.
2013
Stochastic CGL equations without linear dispersion in any space dimension. Zbl 1287.60093
Kuksin, Sergei; Nersesyan, Vahagn
2013
On quantum averaging, quantum KAM, and quantum diffusion. Zbl 1271.81066
Kuksin, S. B.; Neishtadt, A. I.
2013
Mathematics of two-dimensional turbulence. Zbl 1333.76003
Kuksin, Sergei; Shirikyan, Armen
2012
KAM for the nonlinear Schrödinger equation. Zbl 1201.35177
Eliasson, L. Hakan; Kuksin, Sergei B.
2010
Vey theorem in infinite dimensions and its application to KdV. Zbl 1193.37076
Kuksin, Sergei; Perelman, Galina
2010
Damped-driven KdV and effective equations for long-time behaviour of its solutions. Zbl 1231.35205
Kuksin, Sergei B.
2010
Dissipative perturbations of KdV. Zbl 1204.35147
Kuksin, Sergei B.
2010
On reducibility of Schrödinger equations with quasiperiodic in time potentials. Zbl 1176.35141
Eliasson, Håkan L.; Kuksin, Sergei B.
2009
Khasminskii-Whitham averaging for randomly perturbed KdV equation. Zbl 1148.35077
Kuksin, Sergei B.; Piatnitski, Andrey L.
2008
Random kick-forced 3D Navier-Stokes equations in a thin domain. Zbl 1133.76015
Chueshov, Igor; Kuksin, Sergei
2008
Stochastic 3D Navier-Stokes equations in a thin domain and its $$\alpha$$-approximation. Zbl 1143.76422
Chueshov, Igor; Kuksin, Sergei
2008
Four lectures on KAM for the nonlinear Schrödinger equation. Zbl 1140.37021
Eliasson, L. H.; Kuksin, S. B.
2008
Infinite Toeplitz-Lipschitz matrices and operators. Zbl 1140.15025
Eliasson, H. L.; Kuksin, S. B.
2008
On distribution of energy and vorticity for solutions of 2D Navier-Stokes equation with small viscosity. Zbl 1168.35034
Kuksin, Sergei B.
2008
On finite-dimensional projections of distributions for solutions of randomly forced 2D Navier-Stokes equations. Zbl 1177.60059
Agrachev, A.; Kuksin, S.; Sarychev, A.; Shirikyan, A.
2007
Eulerian limit for 2D Navier-Stokes equation and damped/driven KdV equation as its model. Zbl 1161.35461
Kuksin, S. B.
2007
Quasi-linear elliptic differential equations for mappings of manifolds. II. Zbl 1232.58005
Kokarev, Gerasim; Kuksin, Sergei
2007
Rigorous results and conjectures on stationary space-periodic 2D turbulence. Zbl 1171.35445
Kuksin, Sergei B.
2007
Randomly forced nonlinear PDEs and statistical hydrodynamics in 2 space dimensions. Zbl 1099.35083
Kuksin, Sergei B.
2006
Remarks on the balance relations for the two-dimensional Navier-Stokes equation with random forcing. Zbl 1089.76013
Kuksin, Sergei B.
2006
Hamiltonian PDEs. (With an appendix by Dario Bambusi). Zbl 1130.37392
Kuksin, Sergei B.
2006
A family of balance relations for the two-dimensional Navier-Stokes equations with random forcing. Zbl 1064.76027
Kuksin, Sergei; Penrose, Oliver
2005
Poincaré inequalities for maps with target manifold of negative curvature. Zbl 1093.53037
Kappeler, T.; Schroeder, V.; Kuksin, S.
2005
Lectures on Hamiltonian methods in nonlinear PDEs. Zbl 1123.37028
Kuksin, Sergei
2005
The Eulerian limit for 2D statistical hydrodynamics. Zbl 1157.76319
Kuksin, Sergei B.
2004
Randomly forced CGL equation: stationary measures and the inviscid limit. Zbl 1047.35061
Kuksin, Sergei; Shirikyan, Armen
2004
Fifteen years of KAM for PDE. Zbl 1067.37110
Kuksin, Sergei B.
2004
On random attractors for mixing type systems. Zbl 1086.37027
Kuksin, S. B.; Shirikyan, A.
2004
Perturbations of the harmonic map equation. Zbl 1063.58012
Kappeler, T.; Kuksin, S.; Schroeder, V.
2003
Some limiting properties of randomly forced two-dimensional Navier-Stokes equations. Zbl 1060.35106
Kuksin, Sergei; Shirikyan, Armen
2003
Coupling approach to white-forced nonlinear PDEs. Zbl 1021.37044
Kuksin, Sergei; Shirikyan, Armen
2002
A coupling approach to randomly forced nonlinear PDE’s. II. Zbl 1010.60066
Kuksin, Sergei; Piatniski, Andrey; Shirikyan, Armen
2002
Hölder estimates for solutions of parabolic SPDEs. Zbl 1038.60058
Kuksin, S. B.; Nadirashvili, N. S.; Pyatnitskij, A. L.
2002
Ergodic theorems for 2D statistical hydrodynamics. Zbl 1030.37054
Kuksin, Sergei B.
2002
On exponential convergence to a stationary measure for nonlinear PDEs perturbed by random kick-forces, and the turbulence limit. Zbl 1023.37031
Kuksin, Sergei B.
2002
A coupling approach to randomly forced nonlinear PDE’s. I. Zbl 0991.60056
Kuksin, Sergei; Shirikyan, Armen
2001
Ergodicity for the randomly forced 2D Navier-Stokes equations. Zbl 1013.37046
Kuksin, Sergei; Shirikyan, Armen
2001
Analysis of Hamiltonian PDE’s. Zbl 0960.35001
Kuksin, S. B.
2000
Stochastic dissipative PDE’s and Gibbs measures. Zbl 0974.60046
Kuksin, Sergei; Shirikyan, Armen
2000
Spectral properties of solutions for nonlinear PDEs in the turbulent regime. Zbl 0929.35145
Kuksin, S. B.
1999
Stochastic nonlinear Schrödinger equation. I: A priori estimates. Zbl 0984.60070
Kuksin, S. B.
1999
A KAM-theorem for equations of the Korteweg-de Vries type. Zbl 0920.35135
Kuksin, S. B.
1998
Elements of a qualitative theory of Hamiltonian PDEs. Zbl 0967.35123
Kuksin, Sergei B.
1998
On small-denominators equations with large variable coefficients. Zbl 0886.35044
Kuksin, Sergej B.
1997
Oscillation in space-periodic nonlinear Schrödinger equations. Zbl 0874.35113
Kuksin, S. B.
1997
On turbulence in nonlinear Schrödinger equations. Zbl 0912.35143
Kuksin, S. B.
1997
Invariant Cantor manifolds of quasi-periodic oscillations for a nonlinear Schrödinger equation. Zbl 0847.35130
Kuksin, Sergej; Pöschel, Jürgen
1996
Growth and oscillations of solutions of nonlinear Schrödinger equation. Zbl 0862.35112
Kuksin, Sergei B.
1996
Double-periodic solutions of nonlinear Cauchy-Riemann equations. Zbl 0855.58048
Kuksin, Sergej B.
1996
Infinite-dimensional symplectic capacities and a squeezing theorem for Hamiltonian PDE’s. Zbl 0827.35121
Kuksin, Sergej B.
1995
The nonlinear Klein-Gordon equation on an interval as a perturbed sine-Gordon equation. Zbl 0842.35099
Bobenko, Alexander I.; Kuksin, Sergej B.
1995
On squeezing and flow of energy for nonlinear wave equations. Zbl 0834.35086
Kuksin, S. B.
1995
Strong nonresonance of Schrödinger operators and an averaging theorem. Zbl 0885.35119
Kappeler, T.; Kuksin, S.
1995
Small-amplitude solutions of the sine-Gordon equation on an interval under Dirichlet or Neumann boundary conditions. Zbl 0839.35117
Bobenko, A. I.; Kuksin, S. B.
1995
On the inclusion of analytic symplectic maps in analytic Hamiltonian flows and its applications. Zbl 0797.58025
Kuksin, Sergei; Pöschel, Jürgen
1994
KAM-theory for partial differential equations. Zbl 0821.35130
Kuksin, S. B.
1994
Seminar on dynamical systems. Euler International Mathematical Institut, St. Petersburg, Russia, October 14-25 and November 18-29, 1991. Zbl 0782.00078
1994
Nearly integrable infinite-dimensional Hamiltonian systems. Zbl 0784.58028
Kuksin, Sergej B.
1993
On the parametrization of finite-gap solutions by frequency and wavenumber vectors and a theorem of I. Krichever. Zbl 0774.35070
Bikbaev, Ramil F.; Kuksin, Sergej B.
1993
On the inclusion of an almost integrable analytic symplectomorphism into a Hamiltonian flow. Zbl 0931.37030
Kuksin, Sergei B.
1993
A periodic boundary value problem for the sine-Gordon equation, its small Hamiltonian perturbations and KAM deformations of finite-zone tori. Zbl 0771.35052
Bikbaev, R. F.; Kuksin, S. B.
1992
A periodic boundary value problem for the sine-Gordon equation, small Hamiltonian perturbations of it, and KAM-deformations of finite-gap tori. Zbl 0791.35118
Bikbaev, R. F.; Kuksin, S. B.
1992
An infinitesimal Liouville-Arnold theorem as a criterion of reducibility for variational Hamiltonian equations. Zbl 0769.58022
Kuksin, Sergej B.
1992
Perturbation of quasiperiodic solutions of infinite-dimensional Hamiltonian systems. Zbl 0667.58060
Kuksin, S. B.
1989
Perturbation theory for quasiperiodic solutions of infinite-dimensional Hamiltonian systems, and its applications to the Korteweg-de Vries equation. Zbl 0678.58037
Kuksin, S. B.
1989
Reducible equations in variations and perturbations of invariant tori of Hamiltonian systems. Zbl 0684.58013
Kuksin, S. B.
1989
An averaging theorem for distributed conservative systems and its application to von Kármán’s equations. Zbl 0722.73039
Kuksin, S. B.
1989
Conservative perturbations of infinite-dimensional linear systems depending on a vector parameter. Zbl 0688.58033
Kuksin, S. B.
1989
Perturbation of conditionally periodic solutions of infinite-dimensional Hamiltonian systems. Zbl 0662.58036
Kuksin, S. B.
1988
Perturbation theory of conditionally periodic solutions of infinite- dimensional Hamiltonian systems and its application to the Korteweg-de Vries equation. Zbl 0657.58033
Kuksin, S. B.
1988
Hamiltonian perturbations of infinite-dimensional linear systems with an imaginary spectrum. Zbl 0716.34083
Kuksin, S. B.
1987
Hamiltonian perturbations of infinite-dimensional linear systems with imaginary spectrum. Zbl 0631.34069
Kuksin, S. B.
1987
Perturbations of quasilinear elliptic equations and Fredholm manifolds. Zbl 0625.35029
Vishik, M. I.; Kuksin, S. B.
1987
Quasilinear elliptic equations and Fredholm manifolds. Zbl 0599.35041
Vishik, M. I.; Kuksin, S. B.
1985
Generalized solutions of the dynamic problem of perfect elastoplasticity. Zbl 0604.73027
Kuksin, S. B.
1985
Conditions on a discontinuity of solutions of the Prandtl-Reuss equations. Zbl 0584.73040
Kuksin, S. B.
1984
The control problem for the process of elasto-plastic deformation. Zbl 0596.73016
Kuksin, S. B.
1983
Diffeomorphisms of functional spaces corresponding to quasilinear parabolic equations. Zbl 0501.35046
Kuksin, S. B.
1982
An application of monotone semigroups in the theory of perfect elastoplasticity. Zbl 0513.73039
Kuksin, S. B.
1982
...and 4 more Documents
all top 5

### Cited by 650 Authors

 48 Kuksin, Sergeĭ B. 31 Geng, Jiansheng 29 Berti, Massimiliano 28 Procesi, Michela 24 Montalto, Riccardo 22 Xu, Junxiang 21 Bambusi, Dario 21 Kappeler, Thomas 20 Grébert, Benoît 18 Xu, XinDong 17 Si, Jianguo 17 Yuan, Xiaoping 13 Nersesyan, Vahagn 13 Shi, Yanling 13 Shirikyan, Armen R. 13 You, Jiangong 12 Glatt-Holtz, Nathan E. 12 Maspero, Alberto 11 Liu, Jianjun 10 Baldi, Pietro 10 Gao, Meina 10 Li, Yong 10 Mattingly, Jonathan Christopher 9 Bedrossian, Jacob 9 Cong, Hongzi 9 Gentile, Guido 9 Mi, Lufang 9 Topalov, Peter J. 8 Biasco, Luca 8 Bolle, Philippe 8 Boritchev, Alexandre 8 Flandoli, Franco 8 Liang, Zhenguo 8 Lou, Zhaowei 8 Rui, Jie 7 Bourgain, Jean 7 Da Prato, Giuseppe 7 Debussche, Arnaud 7 Dymov, Andrey V. 7 Faou, Erwan 7 Giuliani, Filippo 7 Guardia, Marcel 7 Hairer, Martin 7 Yan, Dongfeng 7 Zhang, Dongfeng 6 Bessaih, Hakima 6 Colliander, James E. 6 Corsi, Livia 6 Haus, Emanuele 6 Li, Jing 6 Razafimandimby, Paul André 6 Thomann, Laurent 6 Wei, Jinlong 6 Xu, Lihu 5 Bakhtin, Yuri Yu. 5 Cerrai, Sandra 5 Coti Zelati, Michele 5 Feola, Roberto 5 Froeschlé, Claude 5 Gao, Yixian 5 Gess, Benjamin 5 Hani, Zaher 5 Ji, Shuguan 5 Kokarev, Gerasim 5 Lega, Elena 5 Li, Dingshi 5 Ren, Xiufang 5 Richards, Geordie 5 Shi, Guanghua 5 Shi, Lin 5 Si, Wen 5 Staffilani, Gigliola 5 Sy, Mouhamadou 5 Wang, Wei-Min 5 Yi, Yingfei 4 Barbu, Viorel 4 Bikbaev, Ramil’ F. 4 Blumenthal, Alex 4 Delort, Jean-Marc 4 Duan, Jinqiao 4 Eliasson, L. Hakan 4 Ferrario, Benedetta 4 Földes, Juraj 4 Gauckler, Ludwig J. 4 Guzzo, Massimiliano 4 Huang, Guan 4 Jakšić, Vojkan 4 Keel, Markus 4 Kukavica, Igor 4 Li, Fuzhi 4 Liu, Wei 4 Luo, Dejun 4 Maiocchi, Alberto Mario 4 Paturel, Eric 4 Peng, Xuhui 4 Peralta-Salas, Daniel 4 Pillet, Claude-Alain 4 Pöschel, Jürgen 4 Punshon-Smith, Sam 4 Schaad, Beat ...and 550 more Authors
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### Cited in 181 Serials

 68 Journal of Differential Equations 67 Communications in Mathematical Physics 35 Journal of Dynamics and Differential Equations 30 Journal of Mathematical Physics 23 Journal of Mathematical Analysis and Applications 23 Discrete and Continuous Dynamical Systems 20 Archive for Rational Mechanics and Analysis 19 Physica D 17 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 16 Journal of Statistical Physics 15 Stochastic Processes and their Applications 13 Journal of Functional Analysis 13 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 13 Stochastic and Partial Differential Equations. Analysis and Computations 11 Nonlinearity 11 Geometric and Functional Analysis. GAFA 11 SIAM Journal on Mathematical Analysis 10 Communications on Pure and Applied Analysis 9 Advances in Mathematics 9 Journal of Nonlinear Science 9 Discrete and Continuous Dynamical Systems. Series B 8 Inventiones Mathematicae 8 Communications in Partial Differential Equations 8 Journal de Mathématiques Pures et Appliquées. Neuvième Série 8 Séminaire Laurent Schwartz. EDP et Applications 7 Applicable Analysis 7 Proceedings of the American Mathematical Society 7 Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Serie IX. Rendiconti Lincei. Matematica e Applicazioni 7 Qualitative Theory of Dynamical Systems 6 Journal d’Analyse Mathématique 6 The Annals of Probability 6 Probability Theory and Related Fields 5 Communications on Pure and Applied Mathematics 5 Journal of Applied Mathematics and Mechanics 5 Mathematical Notes 5 Duke Mathematical Journal 5 Memoirs of the American Mathematical Society 5 Transactions of the American Mathematical Society 5 Chinese Annals of Mathematics. Series B 5 Bulletin of the American Mathematical Society. New Series 5 Journal of Mathematical Sciences (New York) 5 NoDEA. Nonlinear Differential Equations and Applications 5 Taiwanese Journal of Mathematics 5 Journal of the European Mathematical Society (JEMS) 5 Acta Mathematica Sinica. English Series 5 Journal of Dynamical and Control Systems 5 Annales Henri Poincaré 5 Comptes Rendus. Mathématique. Académie des Sciences, Paris 5 Bollettino dell’Unione Matematica Italiana 4 Russian Mathematical Surveys 4 Mathematische Zeitschrift 4 Celestial Mechanics and Dynamical Astronomy 4 Journal of Evolution Equations 4 Dynamical Systems 4 Boundary Value Problems 4 Proceedings of the Steklov Institute of Mathematics 4 Journal of Fixed Point Theory and Applications 4 Science China. Mathematics 3 Reviews in Mathematical Physics 3 Acta Mathematica 3 Applied Mathematics and Optimization 3 Numerische Mathematik 3 Journal of the American Mathematical Society 3 The Annals of Applied Probability 3 Differential Geometry and its Applications 3 Annales de l’Institut Henri Poincaré. Probabilités et Statistiques 3 Russian Journal of Mathematical Physics 3 Mathematical Physics, Analysis and Geometry 3 Chaos 3 Regular and Chaotic Dynamics 3 Communications in Nonlinear Science and Numerical Simulation 3 Nonlinear Analysis. Real World Applications 3 Stochastics and Dynamics 3 Frontiers of Mathematics in China 3 Analysis & PDE 3 Annals of PDE 2 Computers & Mathematics with Applications 2 Physica A 2 ZAMP. Zeitschrift für angewandte Mathematik und Physik 2 Annales de l’Institut Fourier 2 Annali di Matematica Pura ed Applicata. Serie Quarta 2 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie IV 2 Applied Mathematics and Computation 2 Publications Mathématiques 2 Journal of Soviet Mathematics 2 Mathematische Annalen 2 Stochastic Analysis and Applications 2 Acta Applicandae Mathematicae 2 Annals of Global Analysis and Geometry 2 Science in China. Series A 2 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 2 Indagationes Mathematicae. New Series 2 Calculus of Variations and Partial Differential Equations 2 Doklady Mathematics 2 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 2 Infinite Dimensional Analysis, Quantum Probability and Related Topics 2 Communications in Contemporary Mathematics 2 Journal of High Energy Physics 2 Differential Equations 2 Foundations of Computational Mathematics ...and 81 more Serials
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### Cited in 40 Fields

 594 Partial differential equations (35-XX) 472 Dynamical systems and ergodic theory (37-XX) 188 Probability theory and stochastic processes (60-XX) 138 Fluid mechanics (76-XX) 83 Mechanics of particles and systems (70-XX) 61 Ordinary differential equations (34-XX) 41 Quantum theory (81-XX) 34 Statistical mechanics, structure of matter (82-XX) 31 Global analysis, analysis on manifolds (58-XX) 25 Operator theory (47-XX) 24 Mechanics of deformable solids (74-XX) 24 Systems theory; control (93-XX) 20 Differential geometry (53-XX) 19 Numerical analysis (65-XX) 11 Geophysics (86-XX) 9 Functional analysis (46-XX) 6 Optics, electromagnetic theory (78-XX) 5 Measure and integration (28-XX) 5 Harmonic analysis on Euclidean spaces (42-XX) 5 Integral equations (45-XX) 5 Calculus of variations and optimal control; optimization (49-XX) 4 Relativity and gravitational theory (83-XX) 3 Real functions (26-XX) 3 Several complex variables and analytic spaces (32-XX) 3 Difference and functional equations (39-XX) 3 Approximations and expansions (41-XX) 3 Classical thermodynamics, heat transfer (80-XX) 2 General and overarching topics; collections (00-XX) 2 History and biography (01-XX) 2 Number theory (11-XX) 2 Algebraic geometry (14-XX) 2 Group theory and generalizations (20-XX) 2 Topological groups, Lie groups (22-XX) 1 Combinatorics (05-XX) 1 Functions of a complex variable (30-XX) 1 Sequences, series, summability (40-XX) 1 Statistics (62-XX) 1 Astronomy and astrophysics (85-XX) 1 Biology and other natural sciences (92-XX) 1 Information and communication theory, circuits (94-XX)

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