The stability of Kelvin-Stuart cat's eye flows
数学专题报告
报告题目(Title)：The stability of Kelvin-Stuart cat's eye flows.
报告人(Speaker)：林治武（复旦大学数学科学学院）
地点(Place)：后主楼1223
时间(Time)：2024年11月4日14:30-15:30
邀请人(Inviter)：唐仲伟
报告摘要
Kelvin-Stuart vortices are classical mixing layer fows 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 these magnetic islands for co-periodic perturbations, and give the first rigorous proof of the coalescence instability.
主讲人简介
林治武，布朗大学博士，复旦大学教授，相辉学者。从事偏微分方程，动力系统及其应用领域的研究工作，在解的稳定性、长时间行为等方面作出一系列原创性的工作，研究成果发表在《Invent Math》、《Memoirs of AMS》、《CPAM》等国际期刊上。担任SIAM. J. Math. Anal. 等杂志的编委。
