Speaker: Laure Saint-Raymond, Professor of Mathematics at Pierre and Marie Curie University (Paris VI) and École Normale Supérieure
A series of three lectures entitled From Particle Systems to Kinetic Equations.
Lecture I: The low density limit: formal derivation
Consider a deterministic system of N hard spheres of diameter ε. Assume that they are initially independent and identically distributed. Then, in the limit when N→∞ and ε→0 with Nεd-1=1 (Boltzmann-Grad scaling), the one-particle density can be approximated by the solution to the kinetic Boltzmann equation. In particular, particles remain asymptotically independent. In the first lecture, we will present the formal derivation of this low density limit, and discuss two important features, namely the propagation of chaos and the appearance of irreversibility.