Copyright © 2011 Ángel Giménez et al. This is an open access article distributed under the
Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
We study both analytically and numerically the stability of the solutions of the Hébraud-Lequeux equation. This parabolic equation models the evolution for the probability of finding a stress
in a mesoscopic block of a concentrated suspension, a non-Newtonian fluid. We prove a new result concerning the stability of the fixed points of the equation, and pose some conjectures about stability, based on numerical evidence.