Well-Posedness of the Plasma–Vacuum Interface Problem for Ideal Incompressible MHD

摘要

In this paper, we prove the local well-posedness of plasma-vacuum interfaceproblem for ideal incompressible magnetohydrodynamics under the stabilitycondition: the magnetic field $mathbf{h}$ and the vacuum magnetic field$hat{mathbf{h}}$ are non-collinear on the interface(i.e., $|mathbf{h}imeshat{mathbf{h}}|>0$), which was introduced by Trakhinin as a stabilitycondition for the compressible plasma-vacuum interface problem.