Invited talk,2019 京川偏微分方程学术会议,成都绅泰大酒店,2019年5月1-2日。
摘要: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 es timates 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 o f 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.