no. 6
On an incompressible Navier–Stokes/Cahn–Hilliard system with degenerate mobility
Annales de l'I.H.P. Analyse non linéaire, Tome 30 (2013) no. 6, pp. 1175-1190.

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 Grün 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.

DOI : 10.1016/j.anihpc.2013.01.002
Classification : 76T99, 35Q30, 35Q35, 76D03, 76D05, 76D27, 76D45
Mots clés : Two-phase flow, Navier–Stokes equations, Diffuse interface model, Mixtures of viscous fluids, Cahn–Hilliard equation, Degenerate mobility 
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     title = {On an incompressible {Navier{\textendash}Stokes/Cahn{\textendash}Hilliard} system with degenerate mobility},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {1175--1190},
     publisher = {Elsevier},
     volume = {30},
     number = {6},
     year = {2013},
     doi = {10.1016/j.anihpc.2013.01.002},
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}
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Abels, Helmut; Depner, Daniel; Garcke, Harald. On an incompressible Navier–Stokes/Cahn–Hilliard system with degenerate mobility. Annales de l'I.H.P. Analyse non linéaire, Tome 30 (2013) no. 6, pp. 1175-1190. doi : 10.1016/j.anihpc.2013.01.002. http://www.numdam.org/articles/10.1016/j.anihpc.2013.01.002/

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