Space-periodic 2d turbulence and stationary periodic 2d random fields

Lundi 9 juin 2008 14:00-15:00 - S. kuksin - Ecole Polytechnique

Résumé : Consider the 2D Navier-Stokes equations (NSE) on a torus, perturbed by a random force. Assume that the viscosity $\nu$ is small and that the force is scaled in such a way that solutions remain of order one when $\nu$ converges to zero. Then when $\nu$ goes to zero along a sequence, a stationary in time solution $u_\nu(t,x)$ of NSE converges to a space-periodic stationary random field $u_0(t,x)$, formed by solutions of the free 2D Euler equation. The limiting random field, called « the Eulerian limit », describes the stationary space-periodic 2D turbulence. In my talk I will discuss its properties.

Lieu : bât. 425 - 113-115

Space-periodic 2d turbulence and stationary periodic 2d random fields  Version PDF