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 motion of free boundary problem of ideal incompressible MHD

Invited talk, Institute of Applied Physics and Computational Mathematics, Jan. 16, 2017.

Abstract：In this talk, I will discuss the free boundary problem of ideal incompressible MHD flows in Sobolev norms by adopting a geometrical point of view and some quantities such as the second fundamental form and the velocity of the free bondary are estimated. Analogous to the Taylor sign condition for incompressible Euler equations of fluids, we have found a suitable initial condition (i.e.,the generalized Rayleigh-Taylor sign condition) that the outer normal derivative of the total pressure including the fluid and magnetic pressures is negative on the free boundary, under which we proved the a priori properties of solutions of the nonlinear problem. This is an important and necessary step towards the proof of the (local-in-time) well-posedness of the free boundary problem of ideal incompressible MHD system. Some of the results are based on a joint work with T.Luo.

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