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

Details 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

2007-01-29

arxiv.org/abs/math/0701828v2

Mathematics

Analysis of PDEs

9 pages; revised the introduction, added two references and corrected a few misprints

Scientific paper

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.

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