  In this paper we study the three-dimensional two-phase magnetohydrodynamic
interface problem in a bounded domain. The two incompressible fluids are both
Newtonian and the surface tension is considered. We shall use the Galerkin
method to construct the approximate solutions in a bounded domain. Due to the
magnetic field in the magnetohydrodynamic equations, we cannot use the method
of monotone operators to solve the approximate equations. Instead, we will
construct an iterating operator and solve the equations by finding the
fixed-point of the operator. To deal with the free interface, we shall prove
the compactness of the iterating operator and then use the Schauder fixed-point
theorem. The existence of the varifold solution is established by the weak
convergence method.
