# American Institute of Mathematical Sciences

November  2008, 21(4): 1095-1101. doi: 10.3934/dcds.2008.21.1095

## Global well-posedness and a decay estimate for the critical dissipative quasi-geostrophic equation in the whole space

 1 Division of Applied Mathematics, Brown University, 182 George Street, Providence, RI 02912, United States 2 School of Mathematical Sciences, Fudan University, Shanghai 200433, China

Received  July 2007 Revised  February 2008 Published  May 2008

By adapting a method in [11] with a suitable modification, we show that the critical dissipative quasi-geostrophic equations in $R^2$ has global well-posedness with arbitrary $H^1$ initial data. A decay in time estimate for homogeneous Sobolev norms of solutions is also discussed.
Citation: Hongjie Dong, Dapeng Du. Global well-posedness and a decay estimate for the critical dissipative quasi-geostrophic equation in the whole space. Discrete & Continuous Dynamical Systems, 2008, 21 (4) : 1095-1101. doi: 10.3934/dcds.2008.21.1095
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