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

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