A Rigorous Derivation of a Boltzmann System for a Mixture of HardSphere Gases
Abstract
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 nonsymmetric 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.
 Publication:

arXiv eprints
 Pub Date:
 April 2021
 DOI:
 10.48550/arXiv.2104.14480
 arXiv:
 arXiv:2104.14480
 Bibcode:
 2021arXiv210414480A
 Keywords:

 Mathematics  Analysis of PDEs;
 Mathematical Physics
 EPrint:
 41 pages, 1 figure