FM 17-13 (arXiv:1301.2514)

Authors: M. Pulvirenti, C. Saffirio, S. Simonella

Title: On the Validity of the Boltzmann Equation for Short Range Potentials

Abstract: We consider a classical system of point particles interacting by means of a short range potential. We prove that, in the low-density (Boltzmann-Grad) limit, the system behaves, for short times, as predicted by the associated Boltzmann equation. This is a revisitation and an extension of the thesis of King (unpublished), appeared after the well known result of Lanford for hard spheres, and of a recent paper by Gallagher et al (arXiv: 1208.5753v1). Our analysis applies to any stable and smooth potential. In the case of repulsive potentials (with no attractive parts), we estimate explicitly the rate of convergence.