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分析与微分方程研讨会

Analysis on Tollmien-Schlichting wave in the Prandtl-Hartmann Regime

Speaker

杨彤 , 香港城市大学

Time

21 Nov, 10:00 - 10:45

Abstract

In this talk, we will present 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 Chengjie Liu and Zhu Zhang.