Global well-posedness of strong solutions to a two-phase model with magnetic field for large oscillations in three dimensions

Abstract

In this paper, we consider Cauchy problem for a two-phase model with magnetic field in three dimensions. Under some smallness assumptions on the initial data but possibly large oscillations, we obtain the global well-posedness of strong solution as well as its large-time behavior. Compared with Wen and the first author's work [28] where global well-posedness and large time behavior of strong solutions were obtained subject to smallness of initial data in H2 norm, we only need the smallness of initial energy which allows large oscillations of the initial data.