Dynamics of stochastic Zakharov equations

Abstract

The asymptotic behavior of Zakharov equations driven by random force is studied. The force, which is smooth enough and homogeneous in space and white noise in time, acts on both equations of the Zakharov system independently. By some a priori estimates we prove the existence of a solution in energy spaces E1 and E2 via the Galerkin approximation. This solution is defined on the given probability space rather than a martingale solution. Then a global random attractor is constructed in energy space E2 equipped with weak topology. Further the existence of a stationary measure is proved in energy space E2 with usual topology.