In this talk I will discuss the global well-posedness of free interface problems for the incompressible inviscid resistive MHD.  Both plasma-vacuum and plasma-plasma interface problems in a horizontally periodic slab impressed by a uniform transversal magnetic field will be studied.  The free boundary value problems with suitable physical boundary conditions will be formulated and the global well-posedness of both problems with surface tension around the equilibrium is established. Furthermore, the solutions are shown to decay almost exponentially to the equilibrium.  Since the global well-posedness of the free-boundary problems for the incompressible ideal Euler equations with/or without surface tension around the  equilibrium is unknown,  our results here reveal the strong stabilizing effects of the transversal magnetic field and resistivity.  Indeed, one of the key observations here is an induced damping structure for the fluid vorticity due to the resistivity and the transversality of the magnetic field, which turns out to be crucial for both local and global well-posedness of the interfacial problems.  This is a joint work with Yanjin Wang.

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