Hilbert's sixth problem: derivation of fluid equations via Boltzmann's kinetic theory
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866912257136394240 |
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| author | Deng, Yu Hani, Zaher Ma, Xiao |
| author_facet | Deng, Yu Hani, Zaher Ma, Xiao |
| contents | In this paper, we rigorously derive the fundamental PDEs of fluid mechanics, such as the compressible Euler and incompressible Navier-Stokes-Fourier equations, starting from the hard sphere particle systems undergoing elastic collisions. This resolves Hilbert's sixth problem, as it pertains to the program of deriving the fluid equations from Newton's laws by way of Boltzmann's kinetic theory. The proof relies on the derivation of Boltzmann's equation on 2D and 3D tori, which is an extension of our previous work (arXiv:2408.07818). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_01800 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Hilbert's sixth problem: derivation of fluid equations via Boltzmann's kinetic theory Deng, Yu Hani, Zaher Ma, Xiao Analysis of PDEs Mathematical Physics 35Q20, 76P05, 82C40 In this paper, we rigorously derive the fundamental PDEs of fluid mechanics, such as the compressible Euler and incompressible Navier-Stokes-Fourier equations, starting from the hard sphere particle systems undergoing elastic collisions. This resolves Hilbert's sixth problem, as it pertains to the program of deriving the fluid equations from Newton's laws by way of Boltzmann's kinetic theory. The proof relies on the derivation of Boltzmann's equation on 2D and 3D tori, which is an extension of our previous work (arXiv:2408.07818). |
| title | Hilbert's sixth problem: derivation of fluid equations via Boltzmann's kinetic theory |
| topic | Analysis of PDEs Mathematical Physics 35Q20, 76P05, 82C40 |
| url | https://arxiv.org/abs/2503.01800 |