Journal
ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE
Volume 30, Issue 6, Pages 1175-1190Publisher
ELSEVIER SCIENCE BV
DOI: 10.1016/j.anihpc.2013.01.002
Keywords
Two-phase flow; Navier-Stokes equations; Diffuse interface model; Mixtures of viscous fluids; Cahn-Hilliard equation; Degenerate mobility
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Funding
- Transport Processes at Fluidic Interfaces of the German Science Foundation (DFG) [SPP 1506, GA 695/6-1]
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We prove existence of weak solutions for a diffuse interface model for the flow of two viscous incompressible Newtonian fluids in a bounded domain by allowing for a degenerate mobility. The model has been developed by Abels, Garcke and Grun for fluids with different densities and leads to a solenoidal velocity field. It is given by a non-homogeneous Navier Stokes system with a modified convective term coupled to a Cahn-Hilliard system, such that an energy estimate is fulfilled which follows from the fact that the model is thermodynamically consistent. (C) 2013 Elsevier Masson SAS. All rights reserved.
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