On an incompressible Navier–Stokes/Cahn–Hilliard system with degenerate mobility
Annales de l'I.H.P. Analyse non linéaire, Volume 30 (2013) no. 6, p. 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 : https://doi.org/10.1016/j.anihpc.2013.01.002
Classification:  76T99,  35Q30,  35Q35,  76D03,  76D05,  76D27,  76D45
Keywords: Two-phase flow, Navier–Stokes equations, Diffuse interface model, Mixtures of viscous fluids, Cahn–Hilliard equation, Degenerate mobility
@article{AIHPC_2013__30_6_1175_0,
author = {Abels, Helmut and Depner, Daniel and Garcke, Harald},
title = {On an incompressible Navier--Stokes/Cahn--Hilliard system with degenerate mobility},
journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
publisher = {Elsevier},
volume = {30},
number = {6},
year = {2013},
pages = {1175-1190},
doi = {10.1016/j.anihpc.2013.01.002},
zbl = {1347.76052},
mrnumber = {3132421},
language = {en},
url = {http://www.numdam.org/item/AIHPC_2013__30_6_1175_0}
}

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, Volume 30 (2013) no. 6, pp. 1175-1190. doi : 10.1016/j.anihpc.2013.01.002. http://www.numdam.org/item/AIHPC_2013__30_6_1175_0/

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