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

Hongjie Dong

Analysis of PDEs mathscidoc:1912.431022

Arxiv preprint math/0701826, Discrete Contin. Dyn. Syst. A, 26, 1197-1211, 2007.1
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-} is proved. As a corollary, we obtain a global existence result for the critical 2D quasi-geostrophic equations with periodic H^{2-} data. Some decay in time estimates are also provided.
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@inproceedings{hongjie2007dissipative,
  title={Dissipative quasi-geostrophic equations in critical Sobolev spaces: smoothing effect and global well-posedness},
  author={Hongjie Dong},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224211307020738586},
  booktitle={Arxiv preprint math/0701826,  Discrete Contin. Dyn. Syst. A},
  volume={26},
  pages={1197-1211},
  year={2007},
}
Hongjie Dong. Dissipative quasi-geostrophic equations in critical Sobolev spaces: smoothing effect and global well-posedness. 2007. Vol. 26. In Arxiv preprint math/0701826, Discrete Contin. Dyn. Syst. A. pp.1197-1211. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224211307020738586.
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