Two-phase model of crowd propagation

I will talk about the fluid equations used to model pedestrian motion and traffic. I will present the compressible-incompressible Navier-Stokes two phase system describing the flow in the free and in the congested regimes, respectively. I will also show how to approximate such system by the compressible Navier-Stokes equations with singular pressure for the fixed barrier densities and also some recent developments for the barrier densities varying in the space and time.
This is a talk based on several papers in collaboration with: D. Bresch, C. Perrin, P. Degond, P. Minakowski, and L. Navoret.