Some recent advances in the modelling of non-Newtonian fluids

I will present a thermodynamic framework that has been recently put into place that can be used to systematically develop models to describe the response of non-Newtonian fluids. Using the frame-work one can recover models developed by Maxwell, Oldroyd, Burgers and numerous others and also generalizations that automatically meet the demands of the second law of thermodynamics. Since, these new classes of models are able to explain experimental data concerning the flows of complex non-Newtonian fluids it would be worthwhile to study rigorous mathematical questions concerning existence, uniqueness, stability and a numerical analysis of flows of the equations governing the motion of such fluids.