Current research is concerned with the analytical study of physically motivated systems of partial differential equations. So far it has concentrated on several major directions:
- The Q-tensor theory describing liquid crystals
- The Smoluchowski-Doi models describing complex non-Newtonian fluids
- Aspects of classical Newtonian fluids
- The nonlinear Schroedinger equations with potential, used in various applications, in particular in nonlinear optics.