  In this paper, we consider a layer of a viscous incompressible electrically
conducting fluid interacting with the magnetic filed in a horizontally periodic
setting. The upper boundary bounded by a free boundary and below bounded by a
flat rigid interface. We prove the global well-posedness of the problem for
both the case with and without surface tension. Moreover, we show that the
global solution decays to the equilibrium exponentially in the case with
surface tension, however the global solution decays to the equilibrium at an
almost exponential rate in the case without surface tension.
