Invariant measures for stochastic damped 2D Euler equations

Abstract

We study the two-dimensional Euler equations, damped by a linear term and driven by an additive noise. The existence of weak solutions has already been studied; pathwise uniqueness is known for solutions that have vorticity in $L^{\infty }$. In this paper, we prove the Markov property and then the existence of an invariant measure in the space $L^{\infty }$ by means of a Krylov-Bogoliubov's type method, working with the weak$\star$ and the bounded weak$\star$ topologies in $L^{\infty }$.

22 pages. This is the version accepted for publication in Commun. Math. Phys

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