Well-posedness of a multiscale model for concentrated suspensions
| dc.creator | Cancès, Eric | |
| dc.creator | Catto, Isabelle | |
| dc.creator | Gati, Yousra | |
| dc.creator | Bris, Claude Le | |
| dc.date | 2005-03-21 | |
| dc.date.accessioned | 2026-07-07T05:18:11Z | |
| dc.date.available | 2026-07-07T05:18:11Z | |
| dc.description | 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. | |
| dc.description | 1 figure | |
| dc.identifier | https://arxiv.org/abs/math/0503425 | |
| dc.identifier | http://arxiv.org/abs/math/0503425 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/74570 | |
| dc.subject | Analysis of PDEs | |
| dc.subject | 35K55 (Primary) 35K65, 35Q35, 76A05, 76A10 (Secondary) | |
| dc.title | Well-posedness of a multiscale model for concentrated suspensions | |
| dc.type | text |