Local and global strong solutions for SQG in bounded domains

Peter Constantin; Huy Quang Nguyen

doi:10.1016/j.physd.2017.08.008

Local and global strong solutions for SQG in bounded domains

Analysis of PDEs 2018-08-01 v1

Authors: Peter Constantin , Huy Quang Nguyen

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Abstract

We prove local well-posedness for the inviscid surface quasigeostrophic (SQG) equation in bounded domains of $\mathbb{R}^2$ . When fractional Dirichlet Laplacian dissipation is added, global existence of strong solutions is obtained for small data for critical and supercritical cases. Global existence of strong solutions with arbitrary data is obtained in the subcritical cases.

Keywords

surface quasigeostrophic equation bounded domains local well-posedness strong solutions fractional Laplacian critical dissipation global existence

Cite

@article{arxiv.1705.05342,
  title  = {Local and global strong solutions for SQG in bounded domains},
  author = {Peter Constantin and Huy Quang Nguyen},
  journal= {arXiv preprint arXiv:1705.05342},
  year   = {2018}
}

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