Linear Dynamics of the Semi-geostrophic Equations in Eulerian Coordinates on $${\mathbb {R}}^{3}$$
Linear Dynamics of the Semi-geostrophic Equations in Eulerian Coordinates on $${\mathbb {R}}^{3}$$
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$${mathbb {R}}^{3}$$ 上欧拉坐标中的半地转方程的线性动力学
DOI：
10.1007/s00021-021-00574-2
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发表时间：
2021
影响因子：
1.3
通讯作者：
Lisai S
中科院分区：
文献类型：
--
作者：
Lisai S
我们考虑半地转方程的一类稳态解，并推导出围绕这些解的线性动力学。控制这些稳态周围扰动的线性偏微分方程是一个具有 0 阶伪微分算子的输运方程。我们通过引入解的表示公式来研究该方程的适定性，并将结果扩展到调和分布的空间。我们通过研究相关线性化问题的平面波解来研究半地转方程稳态解的稳定性，并讨论准地转方程情况下的差异。
We consider a class of steady solutions of the semi-geostrophic equations onand derive the linearised dynamics around those solutions. The linear PDE which governs perturbations around those steady states is a transport equation featuring a pseudo-differential operator of order 0. We study well-posedness of this equation inintroducing a representation formula for the solutions, and extend the result to the space of tempered distributions on. We investigate stability of the steady solutions of the semi-geostrophic equations by looking at plane wave solutions of the associated linearised problem, and discuss differences in the case of the quasi-geostrophic equations.