Well-posedness of a multiscale model for concentrated suspensions
Gati, Yousra; Catto, Isabelle; Cancès, Eric; Le Bris, Claude (2005), Well-posedness of a multiscale model for concentrated suspensions, Multiscale Modeling & Simulation, 4, 4, p. 1041-1058. http://dx.doi.org/10.1137/040621223
Type
Article accepté pour publication ou publiéLien vers un document non conservé dans cette base
http://hal.archives-ouvertes.fr/hal-00122454/en/Date
2005Nom de la revue
Multiscale Modeling & SimulationVolume
4Numéro
4Éditeur
SIAM
Pages
1041-1058
Identifiant publication
Métadonnées
Afficher la notice complèteRésumé (EN)
In a previous work [math.AP/0305408] three of us have studied a nonlinear parabolic equation arising in the mesoscopic modelling of concentrated suspensions of particles that are subjected to a given time-dependent shear rate. In the present work we extend the model to allow for a more physically relevant situation when the shear rate actually depends on the macroscopic velocity of the fluid, and as a feedback the macroscopic velocity is influenced by the average stress in the fluid. The geometry considered is that of a planar Couette flow. The mathematical system under study couples the one-dimensional heat equation and a nonlinear Fokker-Planck type equation with nonhomogeneous, nonlocal and possibly degenerate, coefficients. We show the existence and the uniqueness of the global-in-time weak solution to such a system.Mots-clés
Cauchy problem; partial differential equation; Couette flow; concentrated suspension; non-Newtonian fluidPublications associées
Affichage des éléments liés par titre et auteur.
-
Legendre, Guillaume; Ciarlet, Patrick (2007) Article accepté pour publication ou publié
-
Ciarlet, Patrick; Legendre, Guillaume (2009) Article accepté pour publication ou publié
-
Catto, Isabelle; Le Bris, Claude; Lions, Pierre-Louis (2001) Article accepté pour publication ou publié
-
Catto, Isabelle; Le Bris, Claude; Lions, Pierre-Louis (2002) Article accepté pour publication ou publié
-
Catto, Isabelle; Le Bris, Claude; Lions, Pierre-Louis (1998) Ouvrage