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Title: Rigorous derivation of a binary-ternary Boltzmann equation for a non ideal gas of hard spheres
Abstract This paper focuses on dynamics of systems of particles that allow interactions beyond binary, and their behavior as the number of particles goes to infinity. More precisely, the paper provides the first rigorous derivation of a binary-ternary Boltzmann equation describing the kinetic properties of a gas consisting of hard spheres, where particles undergo either binary or ternary instantaneous interactions, while preserving momentum and energy. An important challenge we overcome in deriving this equation is related to providing a mathematical framework that allows us to detect both binary and ternary interactions. Furthermore, this paper introduces new algebraic and geometric techniques in order to eventually decouple binary and ternary interactions and understand the way they could succeed one another in time. We expect that this paper can serve as a guideline for deriving a generalized Boltzmann equation that incorporates higher-order interactions among particles.  more » « less
Award ID(s):
2009549 1840314 2052789 1516228
PAR ID:
10597885
Author(s) / Creator(s):
;
Publisher / Repository:
Cambridge University Press
Date Published:
Journal Name:
Forum of Mathematics, Sigma
Volume:
13
ISSN:
2050-5094
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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