Well-posedness of a multiscale model for concentrated suspensions
Abstract
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.
Cite
@article{arxiv.math/0503425,
title = {Well-posedness of a multiscale model for concentrated suspensions},
author = {Eric Cancès and Isabelle Catto and Yousra Gati and Claude Le Bris},
journal= {arXiv preprint arXiv:math/0503425},
year = {2007}
}
Comments
1 figure