Ergodicity of 2D Navier-Stokes equations with random forcing and large viscosity
It is shown that a two-dimensional, incompressible Navier-Stokes equation, forced additively by a Gauss random field, which is white in time, has a unique invariant measure, provided the viscosity is large enough. The proof proceeds by constructing a stationary solution, obtained by starting at a negative time, and then letting the initial time tend to \(-\infty\). The law of this stationary solution is the invariant measure. The method used in this paper is a special case of a method used for the construction of random attractors. The present result can be restated by saying that for large viscosity the attractor is a one-point set. Similar results have recently been obtained by \textit{B. Schmalfuß} [Stochastic Anal. Appl. 17, No. 6, 1075-1101 (1999; Zbl 0944.60071)].
scientific article; zbMATH DE number 1389278