| Issue |
ESAIM: M2AN
Volume 60, Number 2, March-April 2026
|
|
|---|---|---|
| Page(s) | 473 - 494 | |
| DOI | https://doi.org/10.1051/m2an/2026008 | |
| Published online | 24 March 2026 | |
A kinetic model for polyatomic gas with quasi-resonant collisions leading to bi-temperature relaxation processes
1
CERMICS, École des Ponts et Chaussées Institut Polytechnique de Paris & Inria Saclay, Champs-sur-Marne, France
2
Sorbonne Université, Université Paris Cité, CNRS, Laboratoire Jacques-Louis Lions, LJLL, F-75005 Paris, France
3
Université de Rennes, CNRS, IRMAR, UMR 6625, Rennes, France
4
De Vinci Higher Education, De Vinci Research Center, Paris, France
5
Dipartimento di Matematica “F. Casorati”, Università degli Studi di Pavia, Via Ferrata 1, 27100 Pavia, Italy
* Corresponding author: This email address is being protected from spambots. You need JavaScript enabled to view it.
Received:
11
June
2025
Accepted:
19
January
2026
Abstract
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.
Mathematics Subject Classification: 35Q20 / 76P05 / 82C40
Key words: Boltzmann equation / polyatomic gases / resonant collisions / quasi-resonant collisions / near-resonance / Landau-Teller equations
© The authors. Published by EDP Sciences, SMAI 2026
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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