Title：On the free-boundary problem of MHD equations with or without surface tension

Speaker：章俊彦   （约翰•霍普金斯大学）

Time：2019年12月23日         上午    10:10-11:10

Room：东区管理科研楼  1418室

Abstract：I will present the low regularity a priori estimates for the free-boundary incompressible ideal MHD equations. In the case of no surface tension, the smallness of the fluid domain is required in the vorticity estimate to compensate the loss of 1/2-order derivative due to failure of Cauchy invariance. This tells an essential difference from incompressible Euler’s equation. While in the case of nonzero surface tension, the boundary elliptic estimates can help us avoid this difficulty, which shows that surface tension has stronger stabilizing effect than the Taylor sign condition. This is the joint work with Dr. Chenyun Luo. I will also briefly introduce my recent work on the incompressible limit of compressible resistive MHD and discuss the difficulty in the compressible case.