The state of the art of the mathematical and numerical analysis of multi-scale models of complex fluids is reviewed. Issues addressed include well-posedness of the models, convergence analysis of the numerical methods, and the structure of stationary solutions of the Doi-Onsager equation.
"Mathematical Analysis of Multi-Scale Models of Complex Fluids." Commun. Math. Sci. 5 (1) 1 - 51, March 2007.