Discrete and Continuous Dynamical Systems - Series A (DCDS-A)

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

Pages: 1095 - 1101, Volume 21, Issue 4, August 2008      doi:10.3934/dcds.2008.21.1095

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Hongjie Dong - Division of Applied Mathematics, Brown University, 182 George Street, Providence, RI 02912, United States (email)
Dapeng Du - School of Mathematical Sciences, Fudan University, Shanghai 200433, China (email)

Abstract: 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.

Keywords:  Higher regularity, Global well-posedness, Quasi-geostrophic equations.
Mathematics Subject Classification:  Primary: 35Q35, 76B03; Secondary: 86A05.

Received: July 2007;      Revised: February 2008;      Published: May 2008.