Tian Jing - Varifold Solutions to Two-phase Magnetohydrodynamic Equations

We study the motion of two conductive fluids in a bounded container, which is placed in a magnetic field. The two incompressible fluids are both Newtonian and the surface tension is considered. We shall use the Galerkin method to obtain approximate solutions. With the help of solution operators, a suitable iterating operator can be constructed, whose compactness will then be proved to obtain its fixed-point using the Schauder fixed-point theorem. The solution will then be obtained using the weak convergence method. The limits of curvature-related terms will be treated using the theory of varifolds.