A Rigorous Derivation of a Boltzmann System for a Mixture of Hard-Sphere Gases

In this paper, we rigorously derive a Boltzmann equation for mixtures from the many body dynamics of two types of hard sphere gases. We prove that the microscopic dynamics of two gases with different masses and diameters is well defined, and introduce the concept of a two parameter BBGKY hierarchy t...

Full description

Saved in:
Bibliographic Details
Published inarXiv.org
Main Authors Ampatzoglou, Ioakeim, Miller, Joseph K, Pavlović, Nataša
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 29.04.2021
Subjects
BBGKY hierarchy
Boltzmann transport equation
Derivation
Online AccessGet full text

Cover

More Information
Summary:In this paper, we rigorously derive a Boltzmann equation for mixtures from the many body dynamics of two types of hard sphere gases. We prove that the microscopic dynamics of two gases with different masses and diameters is well defined, and introduce the concept of a two parameter BBGKY hierarchy to handle the non-symmetric interaction of these gases. As a corollary of the derivation, we prove Boltzmann's propagation of chaos assumption for the case of a mixtures of gases.
ISSN:2331-8422