Stochastic Navier-Stokes equations for compressible fluids (Q2833068)

The authors consider a Navier-Stokes system for isentropic compressible viscous fluids in three dimensions driven by a multiplicative stochastic forcing. They prove the existence of a solution that is weak in both the PDE and the probabilistic sense. As a driving process, a cylindrical Wiener process is considered. The equations are used to describe the balance of mass and momentum of the flow.NEWLINENEWLINEThe main result is the existence of a weak martingale solution. This solution satisfies an energy inequality that shows the time evolution of the energy compared to the initial energy. The proof of the main result relies on a four-layer approximation scheme in order to deal with the corresponding deterministic counterpart. A stochastic compactness method and a careful identification of a limit procedure are also needed.