Ergodic properties of highly degenerate 2D stochastic Navier-Stokes equations

This Note presents the results from "Ergodicity of the degenerate stochastic 2D Navier-Stokes equation" by M. Hairer and J.C. Mattingly. We study the Navier-Stokes equation on the two-dimensional torus when forced by a finite dimensional Gaussian white noise and give conditions under which the system is ergodic. In particular, our results hold for specific choices of four-dimensional Gaussian white noise. (C) 2004 Academie des sciences. Published by Elsevier SAS. All rights reserved