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

Hongjie Dong

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

Analysis of PDEs 2009-12-09 v2

Authors: Hongjie Dong

Abstract

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.

Keywords

dissipative quasi-geostrophic equations critical sobolev spaces mild solutions regularity global well-posedness decay estimates

Cite

@article{arxiv.math/0701826,
  title  = {Dissipative quasi-geostrophic equations in critical Sobolev spaces: smoothing effect and global well-posedness},
  author = {Hongjie Dong},
  journal= {arXiv preprint arXiv:math/0701826},
  year   = {2009}
}

Comments

Title changed (the original title is: Higher regularity for the critical and super-critical dissipative quasi-geostrophic equations); to appear in DCDS-A, 19 pages

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