Global large solutions for a coupled compressible Navier-Stokes/Allen-Cahn system with initial vacuum

In this paper, we investigate an initial boundary value problem for 1D compressible Navier-Stokes/Allen-Cahn system, which describes the motion of a mixture of two viscous compressible fluids. We establish the global existence and uniqueness of strong and classical solutions of Navier-Stokes/Allen-Cahn system by using the energy estimates, structure of the equations and the properties of one dimension. Here, we emphasize that the initial vacuum is allowed here.