This project is to study the behavior of equations that model complex fluids and to determine criteria for flows to become unstable. Attention will be concentrated on the Oldroyd-B equations and related systems in elastodynamics. These have complicated nonlinear behavior and the existence of global solutions for large data is still not proved. One project is to study the possible development of singularities of the solutions, using both analytical and numerical techniques. Another project is to study the stability and numerical simulations of the solutions of these equations. Some other model equations will also be studied for comparison purposes.
These fluids arise in many applications especially biology and chemical engineering. Many lubricants, plastics and polymers are modeled as such fluids. This work will help understand the dynamics of such materials and develop methods for the numerical simulation of their motion.
