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

Hongjie Dong·Dapeng Du
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Abstract

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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Hongjie Dong, Dapeng Du. 2007-02-13. Global well-posedness and a decay estimate for the critical dissipative quasi-geostrophic equation in the whole space. https://arxiv.org/abs/math/0701828

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