Large Shear Rate Behaviour for the Hébraud-Lequeux Model

Julien Olivier (1)

1 ACMAC - Archimedes Center for Modelling, Analysis and Computation

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 of 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 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.

Mots clés: Limite singulière; rhéologie complexe; modèle cinétique

Domaines: Equations aux dérivées partielles [math.AP]; Physique mathématique [math-ph]

Julien Olivier. Large Shear Rate Behaviour for the Hébraud-Lequeux Model. Science in China Series A: Mathematics, 2012, 55 (2), pp.435 - 452. ⟨10.1007/s11425-011-4350-2⟩. ⟨hal-00650780⟩