From the Boltzmann equation for gas mixture to the two-fluid incompressible hydrodynamic system

2024/08/07 by Fang, Zhendong, Qi, Kunlun
#35Q20 #35Q30 #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Primary 35B25

paper · doi:10.48550/arxiv.2408.03570

Abstract

In this paper, we study the hydrodynamic limit transition from the Boltzmann equation for gas mixtures to the two-fluid macroscopic system. Employing a meticulous dimensionless analysis, we derive several novel hydrodynamic models via the moments' method. For a certain class of scaled Boltzmann equations governing gas mixtures of two species, we rigorously establish the two-fluid incompressible Navier-Stokes-Fourier system as the hydrodynamic limit. This validation is achieved through the Hilbert expansion around the global Maxwellian and refined energy estimates based on the Macro-Micro decomposition.

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