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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

Hongjie Dong 1,

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.
Keywords: quasi-geostrophic equations., global well-posedness, critical and super-critical, higher regularity.
Mathematics Subject Classification: Primary: 35Q35, 76B0.
Citation: Hongjie Dong. Dissipative quasi-geostrophic equations in critical Sobolev spaces: Smoothing effect and global well-posedness. Discrete & Continuous Dynamical Systems, 2010, 26 (4) : 1197-1211. doi: 10.3934/dcds.2010.26.1197
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