We show that the the 2 D quasi-geostrophic equation has global and unique strong solution, when the (large) data belongs in the critical, scale invariant space $\dot{B}^{2-2\al}_{2, \infty}\cap L^{2/(2\al-1)}$.
Global well-posedness of the 3-D full water wave problem
On the global well-posedness of the critical quasi-geostrophic equation
Global well-posedness and scattering for a class of nonlinear Schrodinger equations below the energy space
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