The Stability Principle and global weak solutions of the free surface semi-geostrophic equations in geostrophic coordinates.
The Stability Principle and global weak solutions of the free surface semi-geostrophic equations in geostrophic coordinates.
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地转坐标下自由表面半地转方程的稳定性原理和全局弱解。
DOI：
10.1098/rspa.2018.0787
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发表时间：
2019
期刊：
影响因子：
--
通讯作者：
Cullen MJP
中科院分区：
文献类型：
--
作者：
Cullen MJP
半地转方程在大尺度大气流动模拟中有着广泛的应用。本文证明了在地转坐标系下，具有自由上边界的三维区域中不可压缩半地转方程弱解的整体存在性。证明，基于能量最小化参数最初的灵感来自稳定性原则的研究卡伦，Purser和其他人，使用最佳运输技术以及分析的Hamilton常微分方程空间的概率措施的研究Ambrosio和Gangbo。我们还给出了一个严格的数学框架中的稳定性原则的一般制定。
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.