Sergei B. Kuksin

Q: What Schools Are Affiliated With Sergei B. Kuksin

Sergei B. Kuksin is affiliated with the following schools: Paris-Saclay University, Heriot-Watt University, Paris Diderot University, Moscow State University

Sergei B. Kuksin's AcademicInfluence.com Rankings

Sergei B. Kuksin

Mathematics

#5511

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#7746

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Measure Theory

#3012

World Rank

#3579

Historical Rank

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Mathematics

Why Is Sergei B. Kuksin Influential?

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According to Wikipedia, Sergei Borisovich Kuksin is a French and Russian mathematician, specializing in partial differential equations . Kuksin received his doctorate under the supervision of Mark Vishik at Moscow State University in 1981. He was at the Steklov Institute in Moscow and at the Heriot-Watt University and is a directeur de recherché at the Institut Mathématiques de Jussieu of the Paris Diderot University .

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Sergei B. Kuksin's Published Works

Number of citations in a given year to any of this author's works

Total number of citations to an author for the works they published in a given year. This highlights publication of the most important work(s) by the author

Published Works

Hamiltonian perturbations of infinite-dimensional linear systems with an imaginary spectrum (1987) (319)
KAM for the nonlinear Schrödinger equation (2010) (277)
Stochastic Dissipative PDE's and Gibbs Measures (2000) (153)
On Reducibility of Schrödinger Equations with Quasiperiodic in Time Potentials (2009) (151)
A Coupling Approach¶to Randomly Forced Nonlinear PDE's. I (2001) (141)
KAM for the nonlinear beam equation (2016) (105)
Coupling approach to white-forced nonlinear PDEs (2002) (95)
Ergodicity for the Randomly Forced 2D Navier–Stokes Equations (2001) (73)
On the Inclusion of Analytic Symplectic Maps in Analytic Hamiltonian Flows and Its Applications (1994) (68)
The Eulerian Limit for 2D Statistical Hydrodynamics (2004) (68)
Randomly forced CGL equation: stationary measures and the inviscid limit (2004) (66)
Randomly Forced Nonlinear Pdes and Statistical Hydrodynamics in 2 Space Dimensions (2006) (60)
Spectral Properties of Solutions for Nonlinear PDEs in the Turbulent Regime (1999) (53)
PERTURBATION OF QUASIPERIODIC SOLUTIONS OF INFINITE-DIMENSIONAL HAMILTONIAN SYSTEMS (1989) (51)
Oscillations in space-periodic nonlinear Schrödinger equations (1997) (49)
KAM for the Non-Linear Schr\"odinger Equation (2007) (47)
Khasminskii–Whitham averaging for randomly perturbed KdV equation (2007) (46)
The KdV equation under periodic boundary conditions and its perturbations (2013) (44)
PERTURBATION THEORY FOR QUASIPERIODIC SOLUTIONS OF INFINITE-DIMENSIONAL HAMILTONIAN SYSTEMS, AND ITS APPLICATION TO THE KORTEWEG-DE VRIES EQUATION (1989) (44)
Damped-Driven KdV and Effective Equations for Long-Time Behaviour of its Solutions (2010) (41)
Exponential mixing for a class of dissipative PDEs with bounded degenerate noise (2018) (38)
Vey theorem in infinite dimensions and its application to KdV (2009) (36)
KAM-Theory for Partial Differential Equations (1994) (35)
On Turbulence in Nonlinear Schrödinger Equations (1997) (33)
Random Kick-Forced 3D Navier–Stokes Equations in a Thin Domain (2008) (32)
On squeezing and flow of energy for nonlinear wave equations (1995) (29)
On long-time behavior solutions of nonlinear wave equations (1994) (27)
A Coupling Approach to Randomly Forced Nonlinear PDE's. II (2002) (27)
Stochastic 3D Navier–Stokes equations in a thin domain and its α -approximation (2008) (26)
On finite-dimensional projections of distributions for solutions of randomly forced 2 D Navier – Stokes equations (2007) (25)
KAM theory and the 3D Euler equation (2014) (24)
Weakly nonlinear stochastic CGL equations (2011) (23)
Finite-gap periodic solutions of the KdV equation are non-degenerate (1991) (23)
Seminar on Dynamical Systems (1994) (23)
On Distribution of Energy and Vorticity for Solutions of 2D Navier-Stokes Equation with Small Viscosity (2008) (22)
Growth and oscillations of solutions of nonlinear Schrödinger equation (1996) (22)
Dynamical Systems and Small Divisors (2002) (22)
Fifteen years of KAM for PDE (2004) (22)
On finite-dimensional projections of distributions for solutions of randomly forced PDE's (2006) (21)
Ergodic Theorems for 2D Statistical Hydrodynamics (2002) (21)
A periodic boundary value problem for the Sine-Gordon equation, small Hamiltonian perturbations of it ,and KAM-stability of finite-gap tori (1993) (20)
The effective equation method (2015) (20)
Formal Expansions in Stochastic Model for Wave Turbulence 1: Kinetic Limit (2019) (19)
Stochastic CGL equations without linear dispersion in any space dimension (2012) (19)
Elements of a qualitative theory of Hamiltonian PDEs (1998) (18)
Stochastic nonlinear Schrodinger equation 1. A priori estimates (1999) (18)
On Random Attractors for Mixing Type Systems (2004) (17)
Perturbations of the harmonic map equation (2003) (16)
On quantum averaging, quantum KAM, and quantum diffusion (2012) (16)
Holder Estimates for Solutions of Parabolic SPDEs (2021) (16)
On Exponential Convergence to a Stationary Measure for Nonlinear PDEs Perturbed by Random Kick-Forces, and the Turbulence Limit (2002) (15)
Formal Expansions in Stochastic Model for Wave Turbulence 2: Method of Diagram Decomposition (2019) (14)
KAM for the non-linear Beam equation 2: A normal form theorem (2015) (14)
A Family of Balance Relations for the Two-Dimensional Navier--Stokes Equations with Random Forcing (2005) (14)
Mixing via controllability for randomly forced nonlinear dissipative PDEs (2019) (14)
Derivation of a wave kinetic equation from the resonant-averaged stochastic NLS equation (2015) (13)
On the Zakharov–L’vov Stochastic Model for Wave Turbulence (2019) (12)
The large-period limit for equations of discrete turbulence (2021) (12)
Four lectures on KAM for the non-linear Schrödinger equation (2008) (11)
Time-Averaging for Weakly Nonlinear CGL Equations with Arbitrary Potentials (2014) (11)
One-Dimensional Turbulence and the Stochastic Burgers Equation (2021) (10)
Some limiting properties of randomly forced two-dimensional Navier–Stokes equations (2003) (10)
Exponential mixing for dissipative PDEs with bounded non-degenerate noise (2018) (10)
Eulerian limit for 2D Navier-Stokes equation and damped/driven KdV equation as its model (2007) (10)
Remarks on the Balance Relations for the Two-Dimensional Navier–Stokes Equation with Random Forcing (2006) (9)
PERTURBATIONS OF QUASILINEAR ELLIPTIC EQUATIONS AND FREDHOLM MANIFOLDS (1987) (9)
DOUBLE-PERIODIC SOLUTIONS OF NONLINEAR CAUCHY-RIEMANN EQUATIONS (1996) (9)
Resonant averaging for weakly nonlinear stochastic Schr\"odinger equations (2013) (9)
The limit of small Rossby numbers for randomly forced quasi-geostrophic equation on β-plane (2014) (9)
Global, Local and Dense Non-mixing of the 3D Euler Equation (2019) (9)
Strong nonresonance of Schro¨dinger operators and an averaging theorem (1995) (8)
Small-amplitude solutions of the sine-Gordon equation on an interval under dirichlet or Neumann boundary conditions (1995) (8)
KdV Hamiltonian as a Function of Actions (2011) (8)
On dissipative systems perturbed by bounded random kick-forces (2002) (8)
Asymptotic expansions for some integrals of quotients with degenerated divisors (2017) (8)
KAM for the nonlinear beam equation 1: small-amplitude solutions (2014) (8)
Reducible variational equations and the perturbation of invariant tori of Hamiltonian systems (1989) (8)
ON QUASILINEAR PARABOLIC EQUATIONS (1980) (8)
Resonant averaging for small solutions of stochastic NLS equations (2013) (7)
Quasi-linear elliptic differential equations for mappings of manifolds, II (2006) (7)
DIFFEOMORPHISMS OF FUNCTION SPACES CORRESPONDING TO QUASILINEAR PARABOLIC EQUATIONS (1983) (6)
Quasilinear elliptic differential equations for mappings between manifolds, I (2004) (6)
Coupling approach to white-forced nonlinear PDE (2002) (6)
Quasilinear elliptic equations and Fredholm manifolds (1985) (5)
Hamiltonian Dynamics. Theory and Applications (2005) (5)
Some limiting properties of randomly forced 2D~Navier--Stokes equations (2003) (5)
Rigorous results in space-periodic two-dimensional turbulence (2017) (5)
Derivation of the Kolmogorov-Zakharov equation from the resonant-averaged stochastic NLS equation (2013) (5)
An averaging theorem for distributed conservative systems and its application to von Karman's equations (1989) (5)
Quasilinear elliptic equations for maps between manifolds (2003) (5)
Hamiltonian PDE's (2006) (4)
Analyticity of solutions for quasilinear wave equations and other quasilinear systems (2012) (4)
Conservative perturbations of infinite-dimensional linear systems depending on a vector parameter (1989) (4)
Poincaré Inequalities for Maps with Target Manifold of Negative Curvature (2005) (4)
KAM-persistence of finite-gap solutions (2002) (3)
Asymptotic Properties of Integrals of Quotients when the Numerator Oscillates and the Denominator Degenerates (2018) (3)
Averaging for resonant weakly nonlinear stochastic Schr\"odinger equations (2013) (3)
Rigorous results and conjectures on stationary space-periodic 2D turbulence (2007) (2)
On Averaging and Mixing for Stochastic PDEs (2022) (2)
Resonant averaging for small-amplitude solutions of stochastic nonlinear Schrödinger equations (2017) (2)
A refinement of Heath-Brown's theorem on quadratic forms (2021) (2)
On The Energy Transfer To High Frequencies In The Damped/Driven Nonlinear Schr\"odinger Equation (Extended Version) (2020) (2)
Some remarks on Heath-Brown's theorem on quadratic forms (2021) (2)
Mathematics of Two-Dimensional Turbulence: Preliminaries (2012) (2)
Generalized solutions of the dynamic problem of perfect elastoplasticity (1985) (2)
Chapter 15 - Hamiltonian PDEs (2006) (2)
Introduction \`a l'\'equation de Burgers stochastique et \`a la burgulence (2015) (2)
Kolmogorov’s theory of turbulence and its rigorous 1d model (2021) (2)
Diffeomorphisms of functional spaces that correspond to quasilinear parabolic equations (1983) (2)
Perturbations of one-gap solutions of the Korteweg-de Vries equation (1989) (2)
Three theorems on perturbed KdV (2008) (1)
A KAM theorem for space-multidimensional Hamiltonian PDEs (2016) (1)
DISSIPATIVE PERTURBATIONS OF KdV (2010) (1)
The Bogolyubov--Krylov averaging (2019) (1)
Averaging and mixing for stochastic perturbations of linear conservative systems (2022) (1)
KAM for the non-linear Schrödinger equation - A short presentation (2008) (1)
The smoothness of dependence on initial conditions for solutions of non-linear parabolic equations (1979) (1)
On the energy transfer to high frequencies in the damped/driven nonlinear Schrödinger equation (2020) (1)
On double-periodic solutions of quasilinear Cauchy-Riemann equation (1996) (1)
Conditions on the discontinuity of the Prandtl--Reuss equations solutions (1984) (1)
On exponential convergence to a stationary measure for a class of random dynamical systems (2001) (1)
On the energy transfer to high frequencies in the damped/driven nonlinear Schrödinger equation (2021) (1)
Stochastic CGL equations without linear dispersion in any space dimension (2013) (0)
Marko Iosifovich Vishik (obituary) (2013) (0)
ON THE EIGENFUNCTIONS OF QUASILINEAR ELLIPTIC PROBLEMS (2016) (0)
On the non-degenerate solutions of quasi-linear elliptic boundary value problems (1986) (0)
Notation and conventions (2012) (0)
KAM for the nonlinear beam equation (2016) (0)
Mathematics of Two-Dimensional Turbulence: Uniqueness of stationary measure and mixing (2012) (0)
They Did Not Take It on Faith (2011) (0)
Ergodicity, mixing and KAM (2019) (0)
Workshop on Mathematical Hydrodynamics (2007) (0)
Asymptotical expansions for some singular integrals of rational functions (2017) (0)
D S ] 2 0 O ct 2 01 1 KDV HAMILTONIAN AS FUNCTION OF ACTIONS (2011) (0)
D ec 2 01 7 Rigorous results in space-periodic two-dimensional turbulence (2017) (0)
Conditions on a discontinuity of solutions of the Prandtl-Reiss equations (1984) (0)
THE HOMOLOGICAL EQUATION FOR THE NON-LINEAR SCHRÖDINGER L. H. ELIASSON AND S. B. KUKSIN (2006) (0)
Weak and strong versions of the Kolmogorov 4/5-law for stochastic Burgers equation (2022) (0)
Mathematics of Two-Dimensional Turbulence: Inviscid limit (2012) (0)
Kolmogorov’s theory of turbulence and its rigorous 1d model (2021) (0)
Mathematics of Two-Dimensional Turbulence: Preface (2012) (0)
Two-dimensional Navier–Stokes equations (2012) (0)
An approximation technique for solving the diffusion- and heat-conduction problem for areas with a great number of small defects (1984) (0)
Конференция по математической гидродинамике@@@Workshop on Mathematical Hydrodynamics (2007) (0)
Averaging and mixing for random perturbations of elliptic equilibria (2022) (0)
Ergodicity and limiting theorems (2012) (0)
Solutions to selected exercises (2012) (0)
KAM for NLS (2006) (0)
KdV Hamiltonian as a Function of Actions (2015) (0)
Heuristic algorithm for distribution of periodic tasks among identical computers (1985) (0)
A Vey theorem for nonlinear PDE (2010) (0)
Nonlinear equations of evolutions with small initial data (1980) (0)
Lectures on Hamiltonian Methods in Nonlinear PDEs (2005) (0)
A KAM theorem for space-multidimensional Hamiltonian PDEs (2016) (0)
Some mathematical problems of the batdorf-budiansky-malmeister theory of plasticity (1984) (0)
Remembrances of Walter Craig (2020) (0)
MATHEMATICAL EVENTS: Mark Iosifovich Vishik (on his seventy-fifth birthday) (1997) (0)
Exponential mixing for a class of dissipative PDEs with bounded degenerate noise (2020) (0)
ON THE REGULARITY OF THE SOLUTION OF THE NEUMANN PROBLEM FOR QUASILINEAR PARABOLIC SYSTEMS (2016) (0)
Asymptotic expansions for some integrals of quotients with degenerated divisors (2017) (0)
Mathematical correctness of the boundary lue problems of ideal elastoplasticity (1983) (0)

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What Schools Are Affiliated With Sergei B. Kuksin?

Sergei B. Kuksin is affiliated with the following schools: