二阶Rossby-Haurwitz波的稳定性
偏微分方程分析
2023-07-24 v3
摘要
Rossby-Haurwitz（RH）波是二维旋转球面上不可压缩欧拉方程的重要显式解。本文中，我们证明了二阶RH波的轨道稳定性，证实了A. Constantin与P. Germain在[Arch. Ration. Mech. Anal. 245, 587-644, 2022]中提出的猜想。证明基于变分方法，主要挑战在于为所考虑的解建立合适的变分刻画。在此过程中，固定函数的重排集合起着至关重要的作用。我们还将该方法应用于一阶RH波、Arnold型流以及具有单调绝对涡度的纬向流的稳定性分析。
引用
@article{arxiv.2305.03279,
title = {Stability of degree-2 Rossby-Haurwitz waves},
author = {Daomin Cao and Guodong Wang and Bijun Zuo},
journal= {arXiv preprint arXiv:2305.03279},
year = {2023}
}
备注
In this version, we showed that Theorem 2.3 is optimal for any $\omega\in\mathbb R$ by introducing the generalized RH waves. Stability of zonal flows with monotone absolute vorticity has also been added