From the Boltzmann equation for gas mixture to the two-fluid incompressible hydrodynamic system
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866916349780951040 |
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| author | Fang, Zhendong Qi, Kunlun |
| author_facet | Fang, Zhendong Qi, Kunlun |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2408_03570 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | From the Boltzmann equation for gas mixture to the two-fluid incompressible hydrodynamic system Fang, Zhendong Qi, Kunlun Analysis of PDEs Mathematical Physics Primary 35B25, 35Q30, 35Q20 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. |
| title | From the Boltzmann equation for gas mixture to the two-fluid incompressible hydrodynamic system |
| topic | Analysis of PDEs Mathematical Physics Primary 35B25, 35Q30, 35Q20 |
| url | https://arxiv.org/abs/2408.03570 |