Well-Posedness for Moving Interfaces with Surface Tension in Ideal Compressible MHD

We study the local well-posedness for an interface with surface tension that separates a perfectly conducting inviscid fluid from vacuum. The flow is governed by equations of three-dimensional ideal compressible magnetohydrodynamics (MHD), while vacuum magnetic and electric fields are supposed to satisfy pre-Maxwell equations. tangential interface. This renders nonlinear hyperbolic-elliptic coupled problem characteristic free boundary. introduce some suitable regularization establish solvability tame estimates linearized problem. Combining linear result modified Nash--Moser iteration scheme, we prove existence uniqueness solutions non-collinearity condition required Secchi Trakhinin [Nonlinearity, 27 (2014), pp. 105--169] case zero becomes unnecessary in our result, which verifies stabilizing effect on evolution moving interfaces MHD.