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Elements of a qualitative theory of Hamiltonian PDEs.

Kuksin, Sergei B. — 1998

Documenta Mathematica

On exponential convergence to a stationary measure for a class of random dynamical systems

Sergei B. Kuksin — 2001

Journées équations aux dérivées partielles

For a class of random dynamical systems which describe dissipative nonlinear PDEs perturbed by a bounded random kick-force, I propose a “direct proof” of the uniqueness of the stationary measure and exponential convergence of solutions to this measure, by showing that the transfer-operator, acting in the space of probability measures given the Kantorovich metric, defines a contraction of this space.

Weakly nonlinear stochastic CGL equations

Sergei B. Kuksin — 2013

Annales de l'I.H.P. Probabilités et statistiques

We consider the linear Schrödinger equation under periodic boundary conditions, driven by a random force and damped by a quasilinear damping: $\frac{d}{d t} u + i (- Δ + V (x)) u = ν (Δ u - γ_{R} {| u |}^{2 p} u - i γ_{I} {| u |}^{2 q} u) + \sqrt{ν} η (t, x) . (*)$ The force $η$ is white in time and smooth in $x$ ; the potential $V (x)$ is typical. We are concerned with the limiting, as $ν \to 0$ , behaviour of solutions on long time-intervals $0 \leq t \leq ν^{- 1} T$ , and with behaviour of these solutions under the double limit $t \to \infty$ and $ν \to 0$ . We show that these two limiting behaviours may be described in terms of solutions for the( $*$ ) which is a well posed semilinear...

Rigorous results and conjectures on stationary space-periodic 2D turbulence

Sergei B. Kuksin

Séminaire Équations aux dérivées partielles

We discuss recent results on the inviscid limits for the randomly forced 2D Navier-Stokes equation under periodic boundary conditions, their relevance for the theory of stationary space periodic 2D turbulence and some related conjectures.

Les EDPs hamiltoniennes perturbées et dissipées

Sergei B. Kuksin

Séminaire Laurent Schwartz — EDP et applications

Resonant averaging for weakly nonlinear stochastic Schrödinger equations

Sergei B. Kuksin

Séminaire Laurent Schwartz — EDP et applications

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Currently displaying 1 – 6 of 6

Elements of a qualitative theory of Hamiltonian PDEs.

On exponential convergence to a stationary measure for a class of random dynamical systems

Weakly nonlinear stochastic CGL equations

Rigorous results and conjectures on stationary space-periodic 2D turbulence

Les EDPs hamiltoniennes perturbées et dissipées

Resonant averaging for weakly nonlinear stochastic Schrödinger equations