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

2025/06/04 by Thomas Borsoni, Laurent Boudin, Borsoni, Thomas +5 · 1 citation
Engineering · Mathematics · Physics and Astronomy · #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Gas Dynamics and Kinetic Theory #Mathematical Physics (math-ph) #Optical properties and cooling technologies in crystalline materials #Radiative Heat Transfer Studies

paper · pdf · doi:10.48550/arxiv.2506.03878

openalex publication_date 2025/06/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• On the modelling of polyatomic molecules in kinetic theory
• The Cauchy problem for Boltzmann bi-linear systems: The mixing of monatomic and polyatomic gases
• Compactness property of the linearized Boltzmann operator for a polyatomic gas undergoing resonant collisions
• On the Cauchy problem for Boltzmann equation modelling a polyatomic gas
• New Statistical Models for Kinetic Theory: Methods of Construction
• Kinetic Model for Gases with Internal Degrees of Freedom

Cited by

• Two-temperature fluid models for a polyatomic gas based on kinetic theory for nearly resonant collisions

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