Abstract
In this paper, we study the two phase flow problem with surface tension in the ideal incompressible magnetohydrodynamics. First, we prove the local well-posedness of the two phase flow problem with surface tension. Second, for the initial data satisfying a Syrovatskij type stability condition, we prove that as surface tension tends to zero, the solution of the two phase flow problem with surface tension converges to the solution of the two phase flow problem without surface tension.
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