Influence of vacuum electric field on the stability of a plasma-vacuum interface

We study the free boundary problem for the plasma-vacuum interface in ideal compressible magnetohydrodynamics. Unlike the classical statement, when the vacuum magnetic field obeys the div-curl system of pre-Maxwell dynamics, we do not neglect the displacement current in the vacuum region and consider the Maxwell equations for electric and magnetic fields. We show that a sufficiently large vacuum electric field can make the planar interface violently unstable. We find and analyze a sufficient condition on the vacuum electric field that precludes violent instabilities. Under this condition satisfied at each point of the unperturbed nonplanar plasma-vacuum interface, we prove the well-posedness of the linearized problem in anisotropic weighted Sobolev spaces.