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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2508.03311 |
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| _version_ | 1866915428423434240 |
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| author | Chen, Xinqiu Jiang, Ning Luo, Yi-Long |
| author_facet | Chen, Xinqiu Jiang, Ning Luo, Yi-Long |
| contents | We study the convergence from the multi-species Boltzmann equations to the non-isothermal Maxwell-Stefan system. The global-in-time well-posedness of the Maxwell-Stefan system is first established. The solution is utilized as the fluid quantities to construct a local Maxwellian vector. The Maxwell-Stefan system can be derived from the multi-species Boltzmann equations under diffusive scaling by adding a relation on the total concentration. Different with the classical hydrodynamic limits of the Boltzmann equations, the Maxwellian based on the Maxwell-Stefan system is not a local equilibrium for the mixtures due to cross-interactions. A local coercivity property for the operator linearized around the local Maxwellian is established, based on the explicit spectral gap of the operator linearized around the global equilibrium. The global-in-time solution to the multi-species Boltzmann equations uniform in Knudsen number $\varepsilon$ is established in this scaling, thus the first non-isothermal Maxwell-Stefan asymptotics is rigorously justified. This generalizes Bondesan and Briant's work \cite{briant2021stability} from isothermal to non-isothermal case. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_03311 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The non-isothermal Maxwell-Stefan asymptotics of the multi-species Boltzmann equations Chen, Xinqiu Jiang, Ning Luo, Yi-Long Analysis of PDEs We study the convergence from the multi-species Boltzmann equations to the non-isothermal Maxwell-Stefan system. The global-in-time well-posedness of the Maxwell-Stefan system is first established. The solution is utilized as the fluid quantities to construct a local Maxwellian vector. The Maxwell-Stefan system can be derived from the multi-species Boltzmann equations under diffusive scaling by adding a relation on the total concentration. Different with the classical hydrodynamic limits of the Boltzmann equations, the Maxwellian based on the Maxwell-Stefan system is not a local equilibrium for the mixtures due to cross-interactions. A local coercivity property for the operator linearized around the local Maxwellian is established, based on the explicit spectral gap of the operator linearized around the global equilibrium. The global-in-time solution to the multi-species Boltzmann equations uniform in Knudsen number $\varepsilon$ is established in this scaling, thus the first non-isothermal Maxwell-Stefan asymptotics is rigorously justified. This generalizes Bondesan and Briant's work \cite{briant2021stability} from isothermal to non-isothermal case. |
| title | The non-isothermal Maxwell-Stefan asymptotics of the multi-species Boltzmann equations |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2508.03311 |