2025/08/05 by Chen, Xinqiu, Jiang, Ning, Luo, Yi-Long
#Analysis of PDEs (math.AP) #FOS: Mathematics
paper · doi:10.48550/arxiv.2508.03311
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 ε is established in this scaling, thus the first non-isothermal Maxwell-Stefan asymptotics is rigorously justified. This generalizes Bondesan and Briant's work \citebriant2021stability from isothermal to non-isothermal case.