Online talk

We consider the free-boundary compressible ideal MHD system under Rayleigh-Taylor sign condition. It describes the free-surface motion of a compressible conducting liquid in an electro-magnetic field. The local well-posedness was recently proved by Trakhinin-Wang by using Nash-Moser iteration. We prove the a priori estimate without loss of regularity in the anisotropic Sobolev space. Our proof is based on the combination of the “modified” Alinhac good unknown method, the full utilization of the structure of MHD system and the anisotropy of the function space. This is the joint work with Professor Hans Lindblad.