Analysis of a phase-field model for two-phase compressible fluids

A model describing the evolution of a binary mixture of compressible, viscous, and macroscopically immiscible fluids is investigated. The existence of global-in-time weak solutions for the resulting system coupling the compressible Navier-Stokes equations governing the motion of the mixture with the Allen-Cahn equation for the order parameter is proved without any restriction on the size of initial data.