We raised a Taylor-sign type condition for the free boundary of the incompressible ideal MHD flows with initial bounded smooth domain, and proved the a priori estimates of the solutions to nonlinear system. We also showed the ill-posedness of the solutions in Sobolev spaces when the Taylor-sign type condition is violated. This indicated that the Taylor-sign type condition is much necessary for the well-posedness of the solution in Sobolev spaces to this MHD free boundary problem in bounded smooth domain. This talk is based on the joint works with Tao Luo.

Title: On the free boundary of the incompressible ideal MHD

Speaker: Chengchun HAO (Chinese Academy of Sciences)

10:15-11:00, April 23, 2019 (Jing Zhai 105)