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arXiv · 2408.03570

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

Zhendong Fang·Kunlun Qi
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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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Zhendong Fang, Kunlun Qi. 2024-08-07. From the Boltzmann equation for gas mixture to the two-fluid incompressible hydrodynamic system. https://arxiv.org/abs/2408.03570

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