Asymptotic behavior analysis for non-autonomous quasi-geostrophic equations in R2

In this paper, we investigate the long-time dynamic behavior for non-autonomous quasi-geostrophic equations (QGE) in R-2. It is well-known that these equations in unbounded domains pose additional difficulties which have been of concern for a long time. By establishing some new estimates for a class of general composition functions g(x, u) in Besov space, the uniformly asymptotic compactness of the family of semi processes associated to the QGE with some time-depended external forces F(t, x, ?) is obtained, and the global existence of solutions and of uniform global attractor in Hs(R-2) are also obtained via iterative techniques and commutator estimates. Moreover, the uniform attractor is described by means of its kernel section with asymptotically almost periodic external forces in the sense of Stepanov. It is interesting to applying the estimates for the general composition functions g(x, u) to other models and then generalizing some corresponding previous results on bounded or periodic domains.