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 and Continuous Dynamical Systems, 2008, 21 (4) : 1095-1101. doi: 10.3934/dcds.2008.21.1095
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