Transfert de chaleur dans un fluide de Bingham dont la viscosité dépend de la température

The paper studies the flow of a so-called Bingham fluid, taking into account the variation of viscosity with temperature. The problem is modelled using the technique of variational inequalities of evolution. One proves the existence of a solution in case of a 2-dimensional flow. Questions of uniqueness, and of existence and uniqueness for 3-dimensional flows, are open. The proof relies on fixed-point theory, previous results of the authors for Bingham flows when viscosity does not depend on the temperature and a regularity theorem of Grisvard for linear parabolic equations