American Institute of Mathematical Sciences

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

Convergence to equilibrium of a multiscale model for suspensions

 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.
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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