We study a diffuse interface model for the flow of two viscous incompressible Newtonian fluids of the same density in a bounded domain. The fluids are assumed to be macroscopically immiscible, but a partial mixing in a small interfacial region is assumed in the model. Moreover, diffusion of both components is taken into account. This leads to a coupled Navier-Stokes/Cahn-Hilliard system, which can describe the evolution of droplet formation and collision during the flow. We review some results on existence, uniqueness and regularity of weak and strong solutions in two and three space dimensions. Moreover, we prove stability of local minima of the energy and show existence of a weak global attractor, which is strong if d = 2.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-bc86-0-1,
author = {Helmut Abels},
title = {Longtime behavior of solutions of a Navier-Stokes/Cahn-Hilliard system},
journal = {Banach Center Publications},
volume = {86},
year = {2009},
pages = {9-19},
zbl = {1167.76008},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc86-0-1}
}
Helmut Abels. Longtime behavior of solutions of a Navier-Stokes/Cahn-Hilliard system. Banach Center Publications, Tome 86 (2009) pp. 9-19. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc86-0-1/