Global well-posedness and a decay estimate for the critical dissipative quasi-geostrophic equation in the whole space
Global well-posedness and a decay estimate for the critical dissipative quasi-geostrophic equation in the whole space
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DOI：
10.3934/dcds.2008.21.1095
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发表时间：
2007-01
期刊：
影响因子：
--
通讯作者：
Hongjie Dong;Dapeng Du
中科院分区：
文献类型：
--
作者：
Hongjie Dong;Dapeng Du
研究了$\bR^2$中具有任意$H^1$初始数据的临界耗散拟地转方程。在给出一定的衰减估计后，将该方法应用于[11]，并进行适当的修正，证明了该方法的全局适定性。讨论了解的高阶齐次Sobolev范数的时间估计衰减问题。
We study the critical dissipative quasi-geostrophic equations in $\bR^2$ with arbitrary $H^1$ initial data. After showing certain decay estimate, a global well-posedness result is proved by adapting the method in [11] with a suitable modification. A decay in time estimate for higher order homogeneous Sobolev norms of solutions is also discussed.