  We consider the dynamics of a layer of an incompressible electrically
conducting fluid interacting with the magnetic field in a two-dimensional
horizontally periodic setting. The upper boundary is in contact with the
atmosphere, and the lower boundary is a rigid flat bottom. We prove the global
well-posedness of the inviscid and resistive problem with surface tension
around a non-horizontal uniform magnetic field; moreover, the solution decays
to the equilibrium almost exponentially. One of the key observations here is an
induced damping structure for the fluid vorticity due to the resistivity and
transversal magnetic field.
