Averaging principle for multiscale nonautonomous random 2D Navier-Stokes system

The present paper is a continuation of [30], it complements the earlier results established in [30] and develops a general framework for establishing averaging principles for more complex random dynamical systems. More precisely, in the present paper, we investigate a multiscale nonautonomous random 2D Navier-Stokes system. In order to study asymptotic behavior of the solutions, we establish Stratonovich-Khasminskii averaging principle for the system. It should be emphasized that the similar scheme also works for the Bogoliubov averaging principle, namely, for the two different kinds of averaging principles, we develop a unified methodological framework to establish them. Then, we apply the Stratonovich-Khasminskii averaging principle to multiscale random nonautonomous 2D Navier-Stokes system perturbed by different random forces, such as strong mixing stationary process, Kac-Stroock approximation process, Donsker approximation process, Wong-Zakai approximation process. These random processes have important applications in physics and other natural sciences.