A variational approach for the 2-D semi-geostrophic shallow water equations

A variational approach for the 2-D semi-geostrophic shallow water equations
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二维半地转浅水方程的变分法

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发表时间：
2001
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通讯作者：
M. Cullen
M. Cullen
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文献类型：
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作者：
M. Cullen

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Benamou和Brenier [3]利用Monge输运理论证明了具有刚性边界的三维半地转方程弱解的存在性。本文将结果推广到一个更符合物理性质的自由表面边界条件。这种扩展目前仅适用于二维浅水情况。此外，我们建立了比[3]中可能的更强的时间规律性。* 工作组衷心感谢国家科学基金会赠款DMS 96-22734和DMS-99-70520的支持。
Existence of weak solutions to the 3-D semi-geostrophic equations with rigid boundaries was proved by Benamou and Brenier [3], using Monge transport theory. This paper extends the results to a free surface boundary condition, which is more physically appropriate. This extension is at present for the 2-D shallow water case only. In addition, we establish stronger time regularity than was possible in [3]. ∗WG gratefully acknowledges the support of National Science Foundation grants DMS 96-22734 and DMS-99-70520.