Dissipative quasi-geostrophic equations in critical Sobolev spaces: smoothing effect and global well-posedness

Details Dissipative quasi-geostrophic equations in critical Sobolev spaces: smoothing effect and global well-posedness Dissipative quasi-geostrophic equations in critical Sobolev spaces: smoothing effect and global well-posedness

2007-01-29

arxiv.org/abs/math/0701826v2

Mathematics

Analysis of PDEs

Title changed (the original title is: Higher regularity for the critical and super-critical dissipative quasi-geostrophic equa

Scientific paper

We study the critical and super-critical dissipative quasi-geostrophic
equations in $\bR^2$ or $\bT^2$. Higher regularity of mild solutions with
arbitrary initial data in $H^{2-\gamma}$ is proved. As a corollary, we obtain a
global existence result for the critical 2D quasi-geostrophic equations with
periodic $\dot H^1$ data. Some decay in time estimates are also provided.

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