  We consider the motion of two inviscid, compressible, and electrically
conducting fluids separated by an interface across which there is no fluid flow
in the presence of surface tension. The magnetic field is supposed to be
nowhere tangential to the interface. This leads to the characteristic free
boundary problem for contact discontinuities with surface tension in
three-dimensional ideal compressible magnetohydrodynamics (MHD). We prove the
nonlinear structural stability of MHD contact discontinuities with surface
tension in Sobolev spaces by a modified Nash--Moser iteration scheme. The main
ingredient of our proof is deriving the resolution and tame estimate of the
linearized problem in usual Sobolev spaces of sufficiently large regularity. In
particular, for solving the linearized problem, we introduce a suitable
regularization that preserves the transport-type structure for the linearized
entropy and divergence of the magnetic field.
