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arXiv · 2508.03311

The non-isothermal Maxwell-Stefan asymptotics of the multi-species Boltzmann equations

Xinqiu Chen·Ning Jiang·Yi-Long Luo
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Abstract

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.

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Xinqiu Chen, Ning Jiang, Yi-Long Luo. 2025-08-05. The non-isothermal Maxwell-Stefan asymptotics of the multi-species Boltzmann equations. https://arxiv.org/abs/2508.03311

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