English

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

Analysis of PDEs 2024-08-08 v1 Mathematical Physics math.MP

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.

Keywords

Cite

@article{arxiv.2408.03570,
  title  = {From the Boltzmann equation for gas mixture to the two-fluid incompressible hydrodynamic system},
  author = {Zhendong Fang and Kunlun Qi},
  journal= {arXiv preprint arXiv:2408.03570},
  year   = {2024}
}