Dissipative quasi-geostrophic equations in critical sobolev spaces: Smoothing effect and global well-posedness

Abstract

We study the critical and super-critical dissipative quasi-geostrophic equations in R2 or T2. An optimal local smoothing effect of solutions with arbitrary initial data in H2-γ is proved. As a main application, we establish the global well-posedness for the critical 2D quasi-geostrophic equations with periodic H1 data. Some decay in time estimates are also provided.