  We investigate the general plasma-vacuum interface problems for the ideal
incompressible MHD equations with or without surface tension and prove their
nonlinear local well-posedness in standard Sobolev spaces under either non-zero
surface tension or the stability condition that the magnetic fields are
everywhere non-collinear on the interface. In particular, the results show that
both capillary forces and tangential magnetic fields can stabilize the motion
of the plasma-vacuum interfaces. Moreover, the vanishing surface tension limit
results are established under the Rayleigh-Taylor sign condition or the
non-collinearity condition. All these results hold with no graph assumption on
the free interface.
