# American Institute of Mathematical Sciences

October  2010, 26(4): 1197-1211. doi: 10.3934/dcds.2010.26.1197

## Dissipative quasi-geostrophic equations in critical Sobolev spaces: Smoothing effect and global well-posedness

 1 Division of Applied Mathematics, Brown University, 182 George Street, Providence, RI 02912

Received  July 2008 Revised  February 2009 Published  December 2009

We study the critical and super-critical dissipative quasi-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 the global well-posedness for the critical 2D quasi-geostrophic equations with periodic $H^1$ data. Some decay in time estimates are also provided.
Citation: Hongjie Dong. Dissipative quasi-geostrophic equations in critical Sobolev spaces: Smoothing effect and global well-posedness. Discrete & Continuous Dynamical Systems - A, 2010, 26 (4) : 1197-1211. doi: 10.3934/dcds.2010.26.1197
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