On the evolution of the empirical measure for the Hard-Sphere dynamics

Abstract

We prove that the evolution of marginals associated to the empirical measure of a finite system of hard spheres is driven by the BBGKY hierarchical expansion. The usual hierarchy of equations for $L^1$ measures is obtained as a corollary. We discuss the ambiguities arising in the corresponding notion of microscopic series solution to the Boltzmann-Enskog equation