调和分析和偏微分方程研讨班：Stability and instability of Kelvin-Stuart cat's eyes flows

中科院数学与系统科学研究院

数学研究所

调和分析及其应用研究中心

学术报告

调和分析和偏微分方程研讨班

报告人：Hao Zhu (Nanjing University)

题  目：Stability and instability of Kelvin-Stuart cat's eyes flows

时  间：2023.07.18（星期二）09:30-10:30

地  点：数学院南楼N802

摘  要：Kelvin-Stuart vortices are classical mixing layer flows with many applications in fluid mechanics, plasma physics and planetary rings. We prove that the whole family of Kelvin-Stuart  vortices is nonlinearly stable for co-periodic perturbations, and linearly unstable for multi-periodic or modulational perturbations. Kelvin-Stuart cat's eyes also appear as magnetic islands which are magnetostatic equilibria for the 2D ideal MHD equations in plasmas. We prove  nonlinear stability of the magnetic islands for co-periodic perturbations, and give a rigorous proof of the coalescence instability.