Coupling approach to white-forced nonlinear PDEs

We consider the 2D Navier-Stokes system, perturbed by a white in time random force, such that sufficiently many of its Fourier modes are excited (e.g., all of them are). It is proved that the system has a unique stationary measure and that all solutions exponentially fast converge in distribution to this measure. The proof is based on the same ideas as in our previous works on equations perturbed by random kicks. It applies to a large class of randomly forced PDEs with linear dissipation. (C) 2002 Editions scientifiques et medicales Elsevier SAS. All rights reserved.