Global well-posedness and a decay estimate for the critical dissipative quasi-geostrophic equation in the whole space

Abstract

We study the critical dissipative quasi-geostrophic equations in $\bR^2$ with arbitrary $H^1$ initial data. After showing certain decay estimate, a global well-posedness result is proved by adapting the method in [11] with a suitable modification. A decay in time estimate for higher order homogeneous Sobolev norms of solutions is also discussed.

9 pages; revised the introduction, added two references and corrected a few misprints