A random attractor for the stochastic quasi-geostrophic dynamical system on unbounded domains

In this paper, we prove the existence of a random attractor for the stochastic two-dimensional quasi-geostrophic equation on an unbounded domain, which models a class of large-scale geophysical flows. It is sufficient for a closed absorbing set and the asymptotic compactness of the stochastic system to guarantee the existence of a random attractor for a continuous random dynamical system. Hence, the uniform estimates of solutions including the estimates on the tails of solutions are derived first. Second, the DD-pullback asymptotic compactness of the stochastic system is proved by uniform estimates on solutions for large space and time variables.