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

Hongjie Dong; Dapeng Du

doi:10.3934/dcds.2008.21.1095

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2008, Volume 21, Issue 4: 1095-1101. Doi: 10.3934/dcds.2008.21.1095

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

Hongjie Dong^1, and
Dapeng Du^2,

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

Received: July 2007

Revised: February 2008

Published: October 2008

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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.

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Mathematics Subject Classification: Primary: 35Q35, 76B03; Secondary: 86A05.

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