Stochastic Navier-Stokes equations for compressible fluids

We study the Navier-Stokes equations governing the motion of an isentropic compressible fluid in three dimensions driven by a multiplicative stochastic forcing. In particular, we consider a stochastic perturbation of the system as a function of momentum and density. We establish existence of a so-called finite energy weak martingale solution under the condition that the adiabatic constant satisfies γ> 3/2. The proof is based on a four layer approximation scheme together with a refined stochastic compactness method and a careful identification of the limit procedure.