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We investigate the general plasma-vacuum interface problems for the idealincompressible MHD equations with or without surface tension and prove theirnonlinear local well-posedness in standard Sobolev spaces under either non-zerosurface tension or the stability condition that the magnetic fields areeverywhere non-collinear on the interface. In particular, the results show thatboth capillary forces and tangential magnetic fields can stabilize the motionof the plasma-vacuum interfaces. Moreover, the vanishing surface tension limitresults are established under the Rayleigh-Taylor sign condition or thenon-collinearity condition. All these results hold with no graph assumption onthe free interface.

On the Free Boundary Problems for the Ideal Incompressible MHD Equations