Global well-posedness and a decay estimate for the critical dissipative quasi-geostrophic equation in the whole space
Hongjie Dong - Division of Applied Mathematics, Brown University, 182 George Street, Providence, RI 02912, United States (email)
Abstract: By adapting a method in  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.
Received: July 2007; Revised: February 2008; Available Online: May 2008.
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