We consider the free boundary problem for non-relativistic and relativistic ideal compressible magnetohydrodynamics in two and three spatial dimensions with the total pressure vanishing on the plasma-vacuum interface. We establish the local-in-time existence and uniqueness of solutions to this nonlinear characteristic hyperbolic problem under the Rayleigh-Taylor sign condition on the total pressure. The proof is based on certain tame estimates in anisotropic Sobolev spaces for the linearized problem and a modification of the Nash-Moser iteration scheme. Our result is uniform in the speed of light and appears to be the first well-posedness result for the free boundary problem in ideal compressible magnetohydrodynamics with zero total pressure on the moving boundary.
 Yuri Trakhinin and Tao Wang, Well-posedness of free boundary problem in non-relativistic and relativistic ideal compressible magnetohydrodynamics. Arch. Ration. Mech. Anal. 239 (2021), no. 2,1131-1176.
 Yuri Trakhinin and Tao Wang, Well-posedness for the free-boundary ideal compressible magnetohydrodynamic equations with surface tension. Math. Ann. (2021) doi: 10.1007/s00208-021-02180-z
Associate Prof. Wang Tao (Wuhan University)