Analysis and PDE Seminar——Barotropic instability of shear flows
主 题: Analysis and PDE Seminar——Barotropic instability of shear flows
报告人: Hao Zhu (Chern Institute of Mathematics, Nankai University)
时 间: 2018-04-03 09:00-11:00
地 点: Room 1303, Sciences Building No. 1
Abstract: We consider linear instability of shear flows for incompressible fluids with Coriolis effects. For a class of shear flows including the Sinus one, we prove sharp stability conditions for the whole parameter space, which correct previous results in the fluid literature. Our results are confirmed by more precise numerical computations. 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 steady solutions and the linear inviscid damping near the shear flows. Our proof is based on a careful classification of the neutral limiting modes and the Hamiltonian structure of the linearized fluid equation and an instability index theory recently developed by Lin and Zeng for general Hamiltonian PDEs. This is a joint work with Zhiwu Lin and Jincheng Yang.