Random attractors for a quasi-geostrophic dynamical system under stochastic forcing

Abstract

We consider a dissipative two-dimensional quasi-geostrophic equation, which model a class of large-scale geophysical flows under a stochastic external forcing (the forcing is a Gaussian space-time random field, white noise in time). First, by Faedo-Galerkin method, we prove the existence and uniqueness of the global solution to the initial boundary value problem of the stochastic equation. Second, by studying the asymptotic behaviour of the solution, we obtain the existence of random attractors for the stochastic quasi-geostrophic dynamical system.