报告题目：Linear spectral instability of Hartmann layer via the Tollmien-Schlichting wave

报告人：刘成杰教授（上海交通大学）

报告时间：2021年11月27日10：00-12：00

报告地点：数学与统计学院4号楼302室/ID: 953-375-957

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.

报告人简介：刘成杰，上海交通大学教授，博士生导师，国家高层次青年人才入选者。本科毕业于上海交通大学数学系，在上海交通大学取得博士学位，之后在香港城市大学从事博士后研究。刘成杰的研究领域是非线性偏微分方程以及流体力学中边界层理论的数学分析，主要研究成果发表在《Communications on Pure and Applied Mathematics》、《Advance in Mathematics》、 《Archive for Rational Mechanics and Analysis》、《Journal de Mathématiques Pures et Appliquées》、《SIAM Journal on Mathematical Analysis》等国际著名SCI数学期刊。