UBC DG MP PDE Seminar: Dominik Nowak

We study the dynamics of a test particle in a system of N randomly distributed stationary spherical obstacles (scatterers) in dimensions d≥2. We assume that the test particle's motion is influenced by two contributing factors. One contribution comes from collisions with scatterers, whose interaction potential is modelled by εαU(r/ε), where α∈(0,1/2] and U is radially symmetric and strictly decreasing. The second factor is a long range force field of mean-field type generated by the collection of all scatterers in the system. In the weak coupling regime, we prove that for α∈(0,(d−1)/8) the test particle's probability density converges to the solution of the linear Landau-Vlasov equation as ε→0.

This talk is based on joint work with Chiara Saffirio.