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Global weak solution of planetary geostrophic equations with inviscid geostrophic balance

Jian-Guo Liu University of Maryland Roger Samelson Oregon State University Cheng Wang University of Tennessee

Analysis of PDEs mathscidoc:1702.03062

Applicable Analysis,, 85, (6), 593-605, 2006.6
A reformulation of the planetary geostrophic equations (PGEs) with the inviscid balance equation is proposed and the existence of global weak solutions is established, provided that the mechanical force satisfies an integral constraint. There is only one prognostic equation for the temperature field, and the velocity field is statically determined by the planetary geostrophic balance combined with the incompressibility condition. Furthermore, the velocity profile can be accurately represented as a function of the temperature gradient. In particular, the vertical velocity depends only on the first-order derivative of the temperature. As a result, the bound for the L ∞ (0, t 1 ; L 2 ) ∩ L 2 (0, t 1 ; H 1 ) norm of the temperature field is sufficient to show the existence of the weak solution.
inviscid planetary geostrophic balance, hydrostatic balance, thermal wind equation, global weak solution.
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@inproceedings{jian-guo2006global,
  title={Global weak solution of planetary geostrophic equations with inviscid geostrophic balance},
  author={Jian-Guo Liu, Roger Samelson, and Cheng Wang},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170209092358600983363},
  booktitle={Applicable Analysis,},
  volume={85},
  number={6},
  pages={593-605},
  year={2006},
}
Jian-Guo Liu, Roger Samelson, and Cheng Wang. Global weak solution of planetary geostrophic equations with inviscid geostrophic balance. 2006. Vol. 85. In Applicable Analysis,. pp.593-605. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170209092358600983363.
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