Regularity and qualitative properties for models of complex non-Newtonian fluids

In the first part of the talk I will discuss existence and regularity results for models of complex non-Newtonian fluids containing liquid crystalline polymers. The main technical tool is related to an apriori logarithmic estimate for the 2D Navier-Stokes equations.

In the second part I will consider a simplified version of the system and describe some of its qualitative properties as well as the analytical challenges posed by its study.

The first part is joint work with P Constantin, Ch. Fefferman and E Titi.