A kinetic model for polyatomic gas with quasi-resonant collisions leading to bi-temperature relaxation processes
Fuente:
arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866915324915351552 |
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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 |