On the Generalization of the Hébraud -Lequeux Model to Multidimensional Flows

Julien Olivier (1) , Michael Renardy (2)

1 I2M - Institut de Mathématiques de Marseille
2 Department of Mathematics [Blacksburg]

In this article we build a model for multidimensional flows based on the idea of Hébraud and Lequeux for soft glassy materials. The construction of the model is based on the ideas of Hébraud and Lequeux but care is taken to build a frame indifferent multi-dimensional model. The main goal of this article is to prove that the methodology we have developed to study the well-posedness and the glass transition for the original Hébraud-Lequeux model can be successfully generalized. Thus this work may be used as a starting point for more sophisticated studies in the modeling of general flows of glassy materials.

Domaines: Mathématiques [math]

Julien Olivier, Michael Renardy. On the Generalization of the Hébraud -Lequeux Model to Multidimensional Flows. Archive for Rational Mechanics and Analysis, 2013, 208 (2), pp.569-601. ⟨10.1007/s00205-012-0603-7⟩. ⟨hal-01263132⟩