标题：Barotropic instability of shear flows

报告人：林治武教授（美国乔治亚理工学院）

地点：数学与计算机科学学院4号楼229室

时间：2018年7月6日下午3：30

摘要：We consider barotropic instability of shear flows for incompressible fluids with Coriolis effects. For a class of shear flows, we develop a new method by using the Hamiltonian structures of the linearized equation to find the sharp stability conditions. We study the flow with Sinus profile in details and find the sharp stability boundary in the whole parameter space, which corrects previous results in the fluid literature. The addition of the Coriolis force is found to bring some fundamental changes to the stability of shear flows. Moreover, we study the bifurcation of nontrivial traveling wave solutions and the linear inviscid damping near the shear flows. This is joint work with Hao Zhu and Jincheng Yang.

林治武，1973年出生，本科毕业于北京大学、硕士毕业于日本东京大学，在美国布朗大学取得博士学位，并在著名的应用数学研究中心美国纽约大学柯朗应用数学研究所做博士后研究，现任美国乔治亚理工学院（Georgia Institute of Technology）数学系终身教授。主要研究领域: 数学物理与偏微分方程、流体动力学稳定性及不稳定性理论。共发表20多篇研究论文，其中在数学学科顶级杂志《Inventiones Mathematicae》、数学物理学科一流杂志《Communications on Pure and Applied Mathematics》、《Communications in Mathematical Physics》和《Archive for Rational Mechanics and Analysis》上发表10多篇研究论文。