Title：On the free-boundary problem of MHD equations with or without surface tension
Time：2019年12月23日 上午 10:10-11:10
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.