On the non-Markovian Enskog Equation for Granular Gases

TL;DR

This paper develops a rigorous formalism linking the kinetic evolution of dissipative many-particle systems, specifically granular gases, with non-Markovian Enskog equations and explores their asymptotic behavior in one dimension.

Contribution

It introduces a formal connection between the dual BBGKY hierarchy and the non-Markovian Enskog kinetic equation for granular gases, including their asymptotic analysis.

Findings

Established relationships between microscopic dynamics and kinetic equations for granular gases.

Derived the Boltzmann--Grad asymptotic behavior in one-dimensional systems.

Provided a rigorous framework for non-Markovian kinetic descriptions of dissipative particles.

Abstract

We develop a rigorous formalism for the description of the kinetic evolution of many-particle systems with the dissipative interaction. The relationships of the evolution of a hard sphere system with inelastic collisions described within the framework of marginal observables governed by the dual BBGKY hierarchy and the evolution of states described by the Cauchy problem of the Enskog kinetic equation for granular gases are established. Moreover, we consider the Boltzmann--Grad asymptotic behavior of the constructed non-Markovian Enskog kinetic equation for granular gases in a one-dimensional space.