Abstract

We study the critical and super-critical dissipativequasi-geostrophic equations in $\R^2$ or $\T^2$. An optimal local smoothing effect of solutions with arbitrary initial data in $H^{2-\gamma}$ is proved. As a main application, we establish theglobal well-posedness for the critical 2D quasi-geostrophicequations with periodic $H^1$ data. Some decay in time estimates arealso provided.

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