On the uniqueness of the mild solution of the critical quasi-geostrophic equation

Abstract

We demonstrate that the uniqueness of the mild solution of the two-dimensional quasi-geostrophic equation with the critical dissipation holds in the scaling critical homogeneous Besov space ${\dot{B}}_{\infty ,1}^0$. We consider a solustion of integral equation, and our result does not need regularity assumption.

13 pages