M511

We give an overview on the recent results concerning the compressible Navier-Stokes system subject to stochastic forcing. The theory is based on the concept of dissipative martingale solutions. These solutions are weak in the probabilistic sense as well as in the analytical sense. Moreover, the evolution of the energy can be controlled in terms of the initial energy. We present results on the behavior of solutions in short-time (where unique smooth solutions exists) as well as in the long term (existence of stationary solutions). Finally, we investigate the asymptotics with respect to several parameters of the model based on the energy inequality.

Dominic Breit

Clausthal