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

Abstract 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. To cite this article: M. Hairer, J.C. Mattingly, C. R. Acad. Sci. Paris, Ser. I 339 (2004).

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