Well-Posedness of a Multiscale Model for Concentrated Suspensions

نویسندگان

  • Eric Cancès
  • Isabelle Catto
  • Yousra Gati
  • Claude Le Bris
چکیده

Abstract : In a previous work [1], 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.

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عنوان ژورنال:
  • Multiscale Modeling & Simulation

دوره 4  شماره 

صفحات  -

تاریخ انتشار 2005