论文标题
$ \ mathbb {r}^{3} $在Eulerian坐标中的半缘方程的线性动力学
Linear dynamics of the semi-geostrophic equations in Eulerian coordinates on $\mathbb{R}^{3}$
论文作者
论文摘要
我们考虑了$ \ Mathbb {r}^3 $上半缘方程的一类稳定解决方案，并在这些解决方案周围得出线性化的动力学。支配这些稳态扰动的线性PDE是一个传输方程式，具有伪差异的运算符。我们在$ l^2中研究了该方程式的良好性，该方程式是$ l^2（\ Mathbb {r}^3; \ Mathbb {r}^3） $ \ mathbb {r}^{3} $。我们通过查看线性化问题的平面波解决方案来研究稳定溶液的稳定性，并讨论了准地斑方程的差异。
We consider a class of steady solutions of the semi-geostrophic equations on $\mathbb{R}^3$ and 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 in $L^2(\mathbb{R}^3;\mathbb{R}^3)$ introducing a representation formula for the solutions, and extend the result to the space of tempered distributions on $\mathbb{R}^{3}$. We investigate stability of the steady solutions by looking at plane wave solutions of the linearised problem, and discuss differences in the case of the quasi-geostrophic equations.
