郝成春的个人主页 | Chengchun HAO's Homepage

研究员、博士生导师，中国科学院数学与系统科学研究院 数学研究所 | Professor, Institute of Mathematics, AMSS, CAS

#### On the free boundary problem of incompressible ideal MHD flows

Sun Yat-sen University, Jun. 26, 2015.

**Abstract:** In this talk, I will show the a priori estimates of Sobolev norms for a free boundary problem of the incompressible ideal MHD equations in all physical spatial dimensions $n=2$ and $3$ by adopting a geometrical point of view used in Christodoulou & Lindblad CPAM 2000, and estimating quantities such as the second fundamental form and the velocity of the free surface. We identify the well-posedness condition that the outer normal derivative of the total pressure including the fluid and magnetic pressures is negative on the free boundary, which is similar to the physical condition (Taylor sign condition) for the incompressible Euler equations of fluids. This is based on a joint work with Professor T. Luo.

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