A Rigorous Derivation of a Boltzmann System for a Mixture of Hard-Sphere Gases
Ioakeim Ampatzoglou, Joseph K. Miller, Nataša Pavlović
Source 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 we 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 mixture of gases.
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