报告题目：The stability of Kelvin-Stuart cat's eye flows

报 告 人：林治武教授（美国乔治亚理工大学）

报告时间：2023年5月15日上午10:00-12:00

报告地点：数学院一楼135报告厅

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.

个人简历：林治武，美国布朗大学博士，现为美国佐治亚理工学院教授。从事流体力学, 等离子体及非线性波的偏微分方程模型的研究工作。在解的稳定性，解的长时间动力学行为等方面作出一系列有影响的工作，研究成果发表在Invent. Math., CPAM, Memoirs of AMS, CMP, ARMA等学术期刊上。现担任SIAM. J . Math. Anal. 等杂志的编委。