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arXiv · 2506.03878

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

Thomas Borsoni·Laurent Boudin·Julien Mathiaud·Francesco Salvarani
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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.

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Thomas Borsoni, Laurent Boudin, Julien Mathiaud, Francesco Salvarani. 2025-06-04. A kinetic model for polyatomic gas with quasi-resonant collisions leading to bi-temperature relaxation processes. https://arxiv.org/abs/2506.03878

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