In this paper we study the coupling of the Navier-Stokes equations and the Cahn-Hilliard equation which stands for a model of a multiphase fluid under shear. We first study existence and uniqueness of solutions of the system in dimension 2 and 3 even if the diffusion coefficient is allowed to degenerate. In the last part, an asymptotic stability result is shown.
Publié le : 1999-07-05
Classification:
Shear flow,
Navier-Stokes,
Cahn-Hilliard,
Order parameter,
35K55, 35K65, 76D05, 76E05, 82C26,
[MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP]
@article{hal-00004083,
author = {Boyer, Franck},
title = {Mathematical study of multiphase flow under shear through order parameter formulation},
journal = {HAL},
volume = {1999},
number = {0},
year = {1999},
language = {en},
url = {http://dml.mathdoc.fr/item/hal-00004083}
}
Boyer, Franck. Mathematical study of multiphase flow under shear through order parameter formulation. HAL, Tome 1999 (1999) no. 0, . http://gdmltest.u-ga.fr/item/hal-00004083/