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

Abstract

Abstract. We study the critical dissipative quasi-geostrophic equations in R2 with arbitrary H1 initial data. After showing certain decay estimate, a global well-posedness result is proved by adapting the method in [10]. A decay in time estimate for higher Sobolev norms of solutions is also discussed. 1