中科院数学与系统科学研究院
数学研究所
偏微分方程研讨班
题目/Title: On the incompressible free-boundary MHD with or without surface tension
Speaker：Mr. Junyan Zhang (Johns-Hopkins University, USA)
Time: 16:00-17:00, May 23, 2019 (Thu)
Place: Rm. N602, South Building
Abstract: We present a priori estimates for the incompressible MHD equations in a bounded domain with free moving boundary. In the case of no surface tension, higher regularity of the flow map is required due to a loss of 1/2-order derivative in the low regularity estimates. Due to the lack of Cauchy invariance for MHD, the smallness assumption on the fluid domain is required to control the vorticity of the flow map to compensate this loss. While in the case of nonzero surface tension, the flow map can be controlled by the boundary elliptic estimates owing to the surface tension. Moreover, we show that the magnetic field has certain regularizing effect, allowing us to control the vorticity of the fluid and that of the magnetic field simultaneously. This is the joint work with Dr. Chenyun Luo.