Cahiers du CEREMADE

Unité Mixte de Recherche du C.N.R.S. N°7534
Abstract : In a previous work, 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.
Well-posedness of a multiscale model for concentrated suspensions
CANCES Eric, CATTO Isabelle, GATI Yousra
Université de PARIS - DAUPHINE
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