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Large shear rate behavior for the Hébraud-Lequeux model

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Abstract

The Hébraud-Lequeux model is a model describing the flow of soft glassy material in a simple shear flow configuration. It is given by a kinetic/Fokker-Planck-type equation whose coefficients depend on the shear rate of the experiment. In this paper we want to study what happens to the stationary solutions of this model when the shear rate is asymptotically large. In order to do that, we expand the solution of the equation using singular perturbation tools. In the end, we rigorously prove the estimate of Hébraud and Lequeux that the material asymptotically behaves as a Newtonian fluid.

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Authors and Affiliations

  1. Archimedes Center for Modeling, Analysis and Computation, University of Crete, Iraklio, 71003, Greece

    Julien Olivier

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  1. Julien Olivier
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Correspondence to Julien Olivier.

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Dedicated to the NSFC-CNRS Chinese-French summer institute on fluid mechanics in 2010

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Olivier, J. Large shear rate behavior for the Hébraud-Lequeux model. Sci. China Math. 55, 435–452 (2012). https://doi.org/10.1007/s11425-011-4350-2

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  • DOI: https://doi.org/10.1007/s11425-011-4350-2

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