On the derivation of the linear Boltzmann equation from the nonideal Rayleigh gas
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866916192549076992 |
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| author | Fougères, Florent Thomas |
| author_facet | Fougères, Florent Thomas |
| contents | This paper's objective is to improve the existing proof of the derivation of the Rayleigh--Boltzmann equation from the nonideal Rayleigh gas [6], yielding a far faster convergence rate. This equation is a linear version of the Boltzmann equation, describing the behavior of a small fraction of tagged particles having been perturbed from thermodynamic equilibrium. This linear equation, derived from the microscopic Newton laws as suggested by the Hilbert's sixth problem, is much better understood than the quadratic Boltzmann equation, and even enable results on long time scales for the kinetic description of gas dynamics.The present paper improves the physically poor convergence rate that had been previously proved, into a much more satisfactory rate which is more than exponentially better. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_03266 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the derivation of the linear Boltzmann equation from the nonideal Rayleigh gas Fougères, Florent Thomas Analysis of PDEs Mathematical Physics This paper's objective is to improve the existing proof of the derivation of the Rayleigh--Boltzmann equation from the nonideal Rayleigh gas [6], yielding a far faster convergence rate. This equation is a linear version of the Boltzmann equation, describing the behavior of a small fraction of tagged particles having been perturbed from thermodynamic equilibrium. This linear equation, derived from the microscopic Newton laws as suggested by the Hilbert's sixth problem, is much better understood than the quadratic Boltzmann equation, and even enable results on long time scales for the kinetic description of gas dynamics.The present paper improves the physically poor convergence rate that had been previously proved, into a much more satisfactory rate which is more than exponentially better. |
| title | On the derivation of the linear Boltzmann equation from the nonideal Rayleigh gas |
| topic | Analysis of PDEs Mathematical Physics |
| url | https://arxiv.org/abs/2404.03266 |