The unique solvability of strong solution to the multi-dimensional nonhomogeneous incompressible two-phase magnetohydrodynamic model

Abstract: The present paper studies the initial-boundary value problem of the nonhomogeneous incompressible two-phase magnetohydrodynamic model with Landau potential in a bounded smooth domain in $\mathbb{R}^d$($d = 2, 3$). More precisely, we construct the existence of local in time in three dimension and the global existence of strong solution in two dimension with arbitrary large data and bounded density. In addition, the uniqueness of the solution is proved through the weighted energy estimates, the shift of integrability method and Lagrangian approach.