In this article we build a model for multidimensional flows based on the idea of Hébraud and Lequeux for soft glassy materials. 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
