Mixing and Mixtures in Geo- and Biophysical Flows: A Focus on Mathematical Theory and Numerical Methods

Traffic congestion modelled by the compressible Navier-Stokes equations

Ewelina Zatorska

University College London

We approximate a two–phase model used to describe traffic congestions by the compressible Navier-Stokes equations with a singular pressure term. The weak solutions of the latter approximate weak/measure-valued solutions to the compressible-incompressible two phase system: compressible for the density smaller than some barrier value and incompressible for the barrier value of the density. I will present a result in the multi-dimensional case with heterogeneous barrier and a stronger results for the one-dimensional system. The results are based on joint papers with D. Bresch and with C. Perrin.