American Institute of Mathematical Sciences

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May  2006, 6(3): 449-470. doi: 10.3934/dcdsb.2006.6.449

Convergence to equilibrium of a multiscale model for suspensions

Eric Cancès 1, and  Claude Le Bris 2,

1. 

CERMICS, École Nationale des Ponts et Chaussées, 6 et 8, avenue Blaise Pascal, Cité Descartes - Champs sur Marne, F-77455 Marne La Vallée Cedex 2, France
2. 

CERMICS, École Nationale des Ponts et Chaussées, 6 & 8, avenue Blaise Pascal, 77455 Marne-La-Vallée Cedex 2, France

Received  April 2005 Revised  December 2005 Published  February 2006

We consider a multiscale model describing the flow of a concentrated suspension. The model couples the macroscopic equation of conservation of momentum with a nonlinear nonlocal kinetic equation describing at the microscopic level the rheological behaviour of the fluid. We study the long-time limit of the time-dependent solution. For this purpose, we use the entropy method to prove the convergence to equilibrium of the kinetic equation.
Keywords: long-time limit, non-Newtonian fluid, Couette flow, concentrated suspension, partial differential equation, entropy method., convergence to equilibrium.
Mathematics Subject Classification: 35G25, 35K55 ; Secondary: 76A0.
Citation: Eric Cancès, Claude Le Bris. Convergence to equilibrium of a multiscale model for suspensions. Discrete & Continuous Dynamical Systems - B, 2006, 6 (3) : 449-470. doi: 10.3934/dcdsb.2006.6.449
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