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

Abstract

By adapting a method in [11] with a suitable modification, we showthat the critical dissipative quasi-geostrophic equations in$R^2$ has global well-posedness with arbitrary $H^1$initial data. A decay in time estimate for homogeneous Sobolev normsof solutions is also discussed.