Stationary solutions for stochastic damped Navier-Stokes equations in ${\mathbb{R}}^d$

Abstract

We consider the stochastic damped Navier-Stokes equations in ${\mathbb{R}}^d$ ($d=2,3$), assuming as in our previous work [4] that the covariance of the noise is not too regular, so Itô calculus cannot be applied in the space of finite energy vector fields. We prove the existence of an invariant measure when $d=2$ and of a stationary solution when $d=3$.

31 pages