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

Abstract

In this paper, we consider the global spherically symmetric solutions for the initial boundary value problem of a coupled compressible Navier–Stokes/Allen–Cahn system which describes the motion of two-phase viscous compressible fluids. We prove the existence and uniqueness of global classical solution, weak solution and strong solution under the assumption of spherically symmetry condition for initial data ρ₀ without vacuum state.