On an incompressible Navier-Stokes/Cahn-Hilliard system with degenerate mobility

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.