A kinetic model for polyatomic gas with quasi-resonant collisions leading to bi-temperature relaxation processes

Fuente: arXiv
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Autori principali: Borsoni, Thomas, Boudin, Laurent, Mathiaud, Julien, Salvarani, Francesco
Natura: Preprint
Pubblicazione: 2025
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author Borsoni, Thomas
Boudin, Laurent
Mathiaud, Julien
Salvarani, Francesco
author_facet Borsoni, Thomas
Boudin, Laurent
Mathiaud, Julien
Salvarani, Francesco
contents In this article, we extend the Boltzmann framework for polyatomic gases by introducing quasi-resonant kernels, which relax resonant interactions, for which kinetic and internal energies are separately conserved and lead to equilibrium states with two temperatures. We establish an H-theorem and analyze the quasi-resonant model's asymptotic behaviour, demonstrating a two-phase relaxation process: an initial convergence towards a two-temperature Maxwellian state followed by gradual relaxation of the two temperatures towards each other. Numerical simulations validate our theoretical predictions. The notion of quasi-resonance provides the first rigorous framework of a Boltzmann dynamics for which the distribution is at all times close to a multi-temperature Maxwellian, relaxing towards a one-temperature Maxwellian.
format Preprint
id arxiv_https___arxiv_org_abs_2506_03878
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle A kinetic model for polyatomic gas with quasi-resonant collisions leading to bi-temperature relaxation processes
Borsoni, Thomas
Boudin, Laurent
Mathiaud, Julien
Salvarani, Francesco
Analysis of PDEs
Mathematical Physics
In this article, we extend the Boltzmann framework for polyatomic gases by introducing quasi-resonant kernels, which relax resonant interactions, for which kinetic and internal energies are separately conserved and lead to equilibrium states with two temperatures. We establish an H-theorem and analyze the quasi-resonant model's asymptotic behaviour, demonstrating a two-phase relaxation process: an initial convergence towards a two-temperature Maxwellian state followed by gradual relaxation of the two temperatures towards each other. Numerical simulations validate our theoretical predictions. The notion of quasi-resonance provides the first rigorous framework of a Boltzmann dynamics for which the distribution is at all times close to a multi-temperature Maxwellian, relaxing towards a one-temperature Maxwellian.
title A kinetic model for polyatomic gas with quasi-resonant collisions leading to bi-temperature relaxation processes
topic Analysis of PDEs
Mathematical Physics
url https://arxiv.org/abs/2506.03878