Dissipative Quasi-Geostrophic Equation for Large Initial Data in the Critical Sobolev Space

The critical and super-critical dissipative quasi-geostrophic equations are investigated in . We prove local existence of a unique regular solution for arbitrary initial data in H ^2-2α which corresponds to the scaling invariant space of the equation. We also consider the behavior of the solution near t = 0 in the Sobolev space.