Spherically Symmetric Solutions for a Coupled Compressible Navier-Stokes/Allen-Cahn System

Abstract

In this paper, we consider the initial boundary value problem of a coupled compressible Navier-Stokes/Allen-Cahn system which is described the motion of a mixture of two viscous compressible fluids in 3D. Our aim is to show the existence and uniqueness of local classical solution under the assumption of spherically symmetric condition for initial data ρ0 without vacuum state.