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
TypeArticle accepté pour publication ou publié
External document linkhttp://hal.archives-ouvertes.fr/hal-00122454/en/
Journal nameMultiscale Modeling & Simulation
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Abstract (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.
Subjects / KeywordsCauchy problem; partial differential equation; Couette flow; concentrated suspension; non-Newtonian fluid
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