  In this paper, we propose and analyze a diffuse interface model for
inductionless magnetohydrodynamic fluids. The model couples a convective
Cahn-Hilliard equation for the evolution of the interface, the Navier-Stokes
system for fluid flow and the possion quation for electrostatics. The model is
derived from Onsager's variational principle and conservation laws
systematically. We perform formally matched asymptotic expansions and develop
several sharp interface models in the limit when the interfacial thickness
tends to zero. It is shown that the sharp interface limit of the models are the
standard incompressible inductionless magnetohydrodynamic equations coupled
with several different interface conditions for different choice of the
mobilities. Numerical results verify the convergence of the diffuse interface
model with different mobilitiess.

Analysis of PDEs;Numerical Analysis;Numerical Analysis