Global well-posedness and decay estimates of strong solutions to a two-phase model with magnetic field

In this paper, we consider the Cauchy problem for a two-phase model with magnetic field in three dimensions. The global existence and uniqueness of strong solution as well as the time decay estimates in H-2 (R-3) are obtained by introducing a new linearized system with respect to (n(gamma) - (n)over tilde(gamma), n - (n)over tilde, P - (P)over tilde, u, H) for constants (n)over tilde >= 0 and P >0, and doing some new a priori estimates in Sobolev Spaces to get the uniform upper bound of (n - (n)over tilde, (n(gamma) - (n)over tilde(gamma)) in H-2 (R-3) norm. (c) 2017 Elsevier Inc. All rights reserved.