Asymptotics of stochastic 2D hydrodynamical type systems in unbounded domains

In this paper, we prove a central limit theorem and establish a moderate deviation principle for 2D stochastic hydrodynamical type systems with multiplicative noise in unbounded domains, which covers 2D Navier–Stokes equations, 2D MHD models and the 2D magnetic Bénard problem and also shell models of turbulence. The weak convergence method plays an important role in obtaining the moderate deviation principle.