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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 global well-posedness of both problems with suitable boundary conditions around the equilibrium is established, and the solutions are shown to decay almost exponentially to the equilibrium. The results reveal the strong stabilizing effects of the transversal magnetic field. 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. This is a
joint work with Yanjin Wang.