GLOBAL SOLUTIONS OF A DIFFUSE INTERFACE MODEL FOR THE TWO-PHASE FLOW OF COMPRESSIBLE VISCOUS FLUIDS IN 1D

This paper is concerned with a coupled Navier-Stokes/Cahn-Hilliard system describing a diffuse interface model for the two-phase flow of compressible viscous fluids in a bounded domain in one dimension. We prove the existence and uniqueness of global classical solutions for rho(0) is an element of C-3,C-alpha(I). Moreover, we also obtain the global existence of weak solutions and unique strong solutions for rho(0) is an element of H-1(I) and rho(0) is an element of H-2(I), respectively. In these cases, the initial density function rho(0) has a positive lower bound.