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Main Author: Fougères, Florent Thomas
Format: Preprint
Published: 2024
Subjects:
Online Access:https://arxiv.org/abs/2404.03266
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author Fougères, Florent Thomas
author_facet Fougères, Florent Thomas
contents This paper's objective is to improve the existing proof of the derivation of the Rayleigh--Boltzmann equation from the nonideal Rayleigh gas [6], yielding a far faster convergence rate. This equation is a linear version of the Boltzmann equation, describing the behavior of a small fraction of tagged particles having been perturbed from thermodynamic equilibrium. This linear equation, derived from the microscopic Newton laws as suggested by the Hilbert's sixth problem, is much better understood than the quadratic Boltzmann equation, and even enable results on long time scales for the kinetic description of gas dynamics.The present paper improves the physically poor convergence rate that had been previously proved, into a much more satisfactory rate which is more than exponentially better.
format Preprint
id arxiv_https___arxiv_org_abs_2404_03266
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle On the derivation of the linear Boltzmann equation from the nonideal Rayleigh gas
Fougères, Florent Thomas
Analysis of PDEs
Mathematical Physics
This paper's objective is to improve the existing proof of the derivation of the Rayleigh--Boltzmann equation from the nonideal Rayleigh gas [6], yielding a far faster convergence rate. This equation is a linear version of the Boltzmann equation, describing the behavior of a small fraction of tagged particles having been perturbed from thermodynamic equilibrium. This linear equation, derived from the microscopic Newton laws as suggested by the Hilbert's sixth problem, is much better understood than the quadratic Boltzmann equation, and even enable results on long time scales for the kinetic description of gas dynamics.The present paper improves the physically poor convergence rate that had been previously proved, into a much more satisfactory rate which is more than exponentially better.
title On the derivation of the linear Boltzmann equation from the nonideal Rayleigh gas
topic Analysis of PDEs
Mathematical Physics
url https://arxiv.org/abs/2404.03266