The Enskog Process

TL;DR

This paper proves the existence and uniqueness of solutions to a stochastic system related to the Enskog equation, including conditions for the existence of a density for velocity distributions, advancing kinetic theory understanding.

Contribution

It establishes the existence of weak solutions for a McKean-Vlasov system linked to the Enskog equation and demonstrates conditions for the existence of invariant measure densities.

Findings

Existence of weak solutions under natural conditions.

Uniqueness of the distribution at fixed times.

Gaussian initial conditions lead to invariant measure densities.

Abstract

The existence of a weak solution to a McKean-Vlasov type stochastic differential system corresponding to the Enskog equation of the kinetic theory of gases is established under natural conditions. The distribution of any solution to the system at each fixed time is shown to be unique. The existence of a probability density for the time-marginals of the velocity is verified in the case where the initial condition is Gaussian, and is shown to be the density of an invariant measure.