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...

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Bibliographic Details
Published in:arXiv.org 2021-04
Main Authors: Ampatzoglou, Ioakeim, Miller, Joseph K, Pavlović, Nataša
Format: Article
Language:English
Subjects:
BBGKY hierarchy
Boltzmann transport equation
Derivation
Online Access:Get full text
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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