On a diffuse interface model for a two-phase flow of compressible viscous fluids
Helmut Abels and Eduard Feireisl
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Submission date: 21. Aug. 2007 (revised version: March 2008)
published in: Indiana University mathematics journal, 57 (2008) 2, p. 659-698
DOI number (of the published article): 10.1512/iumj.2008.57.3391
MSC-Numbers: 35Q30, 35Q35, 76N10, 76T99
Keywords and phrases: two-phase flow, free boundary value problems, diffuse interface model, mixtures of viscous fluids, Cahn-Hilliard equation, Navier-Stokes equation
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We consider a model of a binary mixture of compressible, viscous, and macroscopically immiscible fluids based on the diffuse interface approximation, where the difference in concentrations of the two fluids plays the role of the order parameter. The resulting system consists of the compressible Navier-Stokes equations governing the motion of the mixture coupled with the Cahn-Hilliard equation for the order parameter. We prove existence of global-in-time weak (distributional) solutions of the problem without any restriction on the size of initial data.