The APDE seminar on Monday, 10/25, will be given by Junyan Zhang (Johns Hopkins University) online via Zoom from 4:10pm to 5:00pm PST. To participate, email Sung-Jin Oh (sjoh@math.berkeley.edu)

Title: Anisotropic regularity of the free-boundary problem in ideal compressible MHD

Abstract: We consider the free-boundary compressible ideal MHD system under the Rayleigh-Taylor sign condition. The local well-posedness was recently proved by Trakhinin and 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.