Strong Well-Posedness of a Diffuse Interface Model for a Viscous,\n Quasi-Incompressible Two-Phase Flow

2011/01/01 by Helmut Abels, Abels, Helmut · 1 citation
Materials Science · Mathematics · Computer Science · #Solidification and crystal growth phenomena #Navier-Stokes equation solutions #Advanced Mathematical Modeling in Engineering

paper · pdf · doi:10.48550/arxiv.1103.6211

Abstract

We study a diffuse interface model for the flow of two viscous incompressible\nNewtonian fluids in a bounded domain. The fluids are assumed to be\nmacroscopically immiscible, but a partial mixing in a small interfacial region\nis assumed in the model. Moreover, diffusion of both components is taken into\naccount. In contrast to previous works, we study a model for the general case\nthat the fluids have different densities due to Lowengrub and Truskinovski.\nThis leads to an inhomogeneous Navier-Stokes system coupled to a Cahn-Hilliard\nsystem, where the density of the mixture depends on the concentration, the\nvelocity field is no longer divergence free, and the pressure enters the\nequation for the chemical potential. We prove existence of unique strong\nsolutions for the non-stationary system for sufficiently small times.\n

Cited by

• Weak solutions and incompressible limit of a quasi-incompressible Navier--Stokes/Cahn--Hilliard model for viscous two-phase flows

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