The Enskog process for hard and soft potentials

TL;DR

This paper extends the Enskog process framework to include a broader class of collision kernels, including hard and soft potentials, by establishing existence through particle approximation methods.

Contribution

It introduces a generalized Enskog process for diverse collision kernels, expanding the applicability of the stochastic process model for dense gases.

Findings

Existence of the Enskog process for a wider class of potentials

Particle approximation method for binary collisions

Extension of previous models to hard and soft potentials

Abstract

The density of a moderately dense gas evolving in a vacuum is given by the solution of an Enskog equation. Recently we have constructed in [ARS17] the stochastic process that corresponds to the Enskog equation under suitable conditions. The Enskog process is identified as the solution of a McKean-Vlasov equation driven by a Poisson random measure. In this work, we continue the study for a wider class of collision kernels that includes hard and soft potentials. Based on a suitable particle approximation of binary collisions, the existence of an Enskog process is established.