Linear spectral instability of Hartmann layer via the Tollmien-Schlichting wave
数学专题报告
报告题目(Title)：Linear spectral instability of Hartmann layer via the Tollmien-Schlichting wave
报告人(Speaker)：刘成杰 教授（上海交通大学数学科学学院）
地点(Place)：腾讯会议号：667946711 (无需密码)
时间(Time)：2021年12月7日下午2:00-3:00
邀请人(Inviter)：许孝精
报告摘要
In this talk, I will show the instability induced by the Tollmien-Schlichting wave governed by the MHD system in the Prandtl-Hartmann regime. The interaction of the inviscid mode and viscous mode that leads to the instability is analyzed by the introduction of a new decomposition of the Orr-Sommerfeld operator on the velocity and magnetic fields. The critical Gevrey index for the instability is justified by constructing the growing mode in the essential frequency and it is shown to be the same as the incompressible Navier-Stokes equations in the Prandtl regime. This result justifies rigorously the physical understanding that the transverse magnetic field to the boundary in the Prandtl-Hartmann regime has no extra stabilizing effect on the Tollmien-Schlichting wave. This is a joint work with Prof. Tong Yang and Dr. Zhu Zhang.
