The Stability Principle and global weak solutions of the free surface semi-geostrophic equations in geostrophic coordinates

机译：根瘤坐标中自由表面半地嗜酸性方程的稳定性原理和全局弱解

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The semi-geostrophic equations are used widely in the modelling of large-scale atmospheric flows. In this note, we prove the global existence of weak solutions of the incompressible semi-geostrophic equations, in geostrophic coordinates, in a three-dimensional domain with a free upper boundary. The proof, based on an energy minimization argument originally inspired by the Stability Principle as studied by Cullen, Purser and others, uses optimal transport techniques as well as the analysis of Hamiltonian ODEs in spaces of probability measures as studied by Ambrosio and Gangbo. We also give a general formulation of the Stability Principle in a rigorous mathematical framework.

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期刊名称 Proceedings. Mathematical Physical and Engineering Sciences
作者
M. J. P. Cullen; T. Kuna; B. Pelloni; M. Wilkinson;
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作者单位

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年(卷),期 -1(475),2229
年度 -1
页码 -1
总页数 15
原文格式 PDF
正文语种
中图分类病理学;
关键词
semi-geostrophic equations; optimal transport; Wasserstein spaces; stabilitycriteria;

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专利

1. Global weak solution of planetary geostrophic equations with inviscid geostrophic balance [J] . JIAN-GUO LIU, ROGER SAMELSON, CHENG WANG Applicable Analysis . 2006,第6a7期

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2. Existence of global weak solutions for a 2D viscous shallow water equations and convergence to the quasi-geostrophic model [J] . Bresch D., Desjardins B. Communications in Mathematical Physics . 2003,第1a2期

机译：二维粘性浅水方程整体弱解的存在性及拟地转模型的收敛性
3. Existence of Global Weak Solutions for a 2D Viscous Shallow Water Equations and Convergence to the Quasi-Geostrophic Model [J] . Didier Bresch, Benoît Desjardins Communications in Mathematical Physics . 2003,第1a2期

机译：二维粘性浅水方程整体弱解的存在性与拟地转模型的收敛性
4. POROUS MEDIA EQUATIONS, FAST DIFFUSIONS EQUATIONS AND THE EXISTENCE OF GLOBAL WEAK SOLUTION FOR THE QUASI-SOLUTIONS OF COMPRESSIBLE NAVIER-STOKES EQUATIONS [C] . BORIS HASPOT International Conference on Hyperbolic Problems . 2014

机译：多孔介质方程，快速扩散方程以及压缩Navier-Stokes方程准溶液的全局弱解决方案
5. Global regularity or finite time singularity of the surface quasi-geostrophic equations. [D] . Sharma, Ramjee Prasad. 2010

机译：地准准地层方程的整体正则性或有限时间奇异性。
6. On the geometry of solutions of the quasi-geostrophic and Euler equations [O] . Diego Cordoba 1997

机译：拟地转方程和欧拉方程的解的几何
7. Smooth solutions of the surface semi-geostrophic equations [O] . Stefania Lisai, Mark Wilkinson 2019

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8. Global Weak Solution of Planetary Geostrophic Equations with Inviscid Geostrophic Balance. [R] . Liu, J., Samelson, R., Wang, C. 2006

机译：具有Inviscid地理平衡的行星地理方程的整体弱解。

The Stability Principle and global weak solutions of the free surface semi-geostrophic equations in geostrophic coordinates

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