Global well-posedness of dissipative quasi-geostrophic equations in critical spaces

Abstract

We prove global well-posedness for the dissipative quasi-geostrophic equation with initial data in critical Besov spaces B p , q 1 + 2 p − 2 α B^{1+ {2 \over p}-2\alpha }_{p,q} , 0 > α ≤ 1 0> \alpha \leq 1 , provided that the B p , q 1 + 2 p − 2 α B^{1+ {2 \over p}-2\alpha }_{p,q} norm of the initial data is sufficiently small compared with the dissipative coefficient κ \kappa .