Hilbert's sixth problem: derivation of fluid equations via Boltzmann's kinetic theory
2025/03/03 by Yu Deng, Zaher Hani, Deng, Yu +3 · 28 voices · 10 citations
Physics and Astronomy · Mathematics · #Advanced Thermodynamics and Statistical Mechanics #Quantum Mechanics and Applications #Gas Dynamics and Kinetic Theory
paper · pdf · doi:10.48550/arxiv.2503.01800
Abstract
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).
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- Hilbert's sixth problem: derivation of fluid equations via Boltzmann's theory [hn, 154 points, 99 comments]
- This is a really cool result. I hope it holds up through review. It's exciting even to see somebody plausibly claim it. arxiv.org/pdf/2503.01800 [bsky, 3 points, 1 comments]
- Hilbert 6th problem: derivation of fluid equations via Boltzmann kinetic theory [hn, 3 points, 0 comments]
- Hilbert's sixth problem: derivation of fluid equations via Boltzmann's kinetic theory arxiv.org/abs/2503.01800 [bsky, 2 points, 0 comments]
- Hilbert's sixth problem: derivation of fluid equations via Boltzmann's theory [hn, 2 points, 1 comments]
- `we rigorously derive the fundamental PDEs of fluid mechanics..starting from the hard sphere particle systems undergoing elastic collisions. This resolves Hilbert's sixth problem, as it pertains to th [bsky, 1 points, 1 comments]
- HILBERT’S SIXTH PROBLEM: DERIVATION OF FLUID EQUATIONS VIA BOLTZMANN’S KINETIC THEORY arxiv.org/pdf/2503.01800 [bsky, 1 points, 0 comments]
- arxiv.org/abs/2503.01800 [bsky, 1 points, 0 comments]
- Et sinon, y a ceux-la a verifier aussi 🤣 : 6eme probleme de Hilbert, arxiv.org/abs/2503.01800, et conjecture de Kaleya en dimension 3, arxiv.org/abs/2502.17655, mais ca va prendre plus de 2h… [bsky, 1 points, 0 comments]
- I don't claim to understand academic math. But it's exciting to see the Fields Medal being awarded to new connections between Newton and Boltzmann. doi.org/10.48550/arX... [bsky, 1 points, 0 comments]
- Hilbert's Sixth Problem Resolved [hn, 1 points, 0 comments]
- Hilbert's 6.problem:derivation of fluid equations via Boltzmann's kinetic theory [hn, 1 points, 0 comments]
- Hilbert's sixth problem: derivation of fluid equations via Boltzmann's theory https://arxiv.org/abs/2503.01800 https://news.ycombinator.com/item?id=44439242 [bsky, 0 points, 0 comments]
- Hilbert's sixth problem: derivation of fluid equations via Boltzmann's theory https://arxiv.org/abs/2503.01800 [bsky, 0 points, 0 comments]
- Hilbert's sixth problem: derivation of fluid equations via Boltzmann's theory View Article | Join the HN Conversation Summary of HN discussion 🧵👇 #hacker-news [bsky, 0 points, 1 comments]
- Hilbert's sixth problem: derivation of fluid equations via Boltzmann's theory https://arxiv.org/abs/2503.01800 [comments] [51 points] [bsky, 0 points, 0 comments]
- arxiv.org/abs/2503.01800 [bsky, 0 points, 0 comments]
- Hilbert's sixth problem: derivation of fluid equations via Boltzmann's theory https://arxiv.org/abs/2503.01800 (https://news.ycombinator.com/item?id=44439242) [bsky, 0 points, 0 comments]
- ⚡ Hackernews Top story: Hilbert's sixth problem: derivation of fluid equations via Boltzmann's theory [bsky, 0 points, 0 comments]
- [2503.01800] Hilbert's sixth problem: derivation of fluid equations via Boltzmann's kinetic theory arxiv.org/abs/2503.01800 [bsky, 0 points, 0 comments]
- "Hilbert’s sixth problem: derivation of fluid equations via Boltzmann’s kinetic theory Yu Deng, Zaher Hani, Xiao Ma - arxiv"3 Mar 2025 arxiv.org/abs/2503.01800 [bsky, 0 points, 1 comments]
- https://bsky.app/profile/buzzing.cc.web.brid.gy/post/3lsy736krutu2 [bsky, 0 points, 0 comments]
- Hilbert's sixth problem: derivation of fluid equations via Boltzmann's theory https://arxiv.org/abs/2503.01800 (https://news.ycombinator.com/item?id=44439242) [bsky, 0 points, 0 comments]
- A first step of axiomatisation of physics of fluids arxiv.org/abs/2503.018... [bsky, 0 points, 0 comments]
- Derivaram as EDPs fundamentais da mecânica dos fluidos usando a teoria cinética de Boltzmann (colisões elásticas), tô chocada. Estão revisando pra ver se o sexto problema de Hilbert foi solucionado, t [bsky, 0 points, 1 comments]
- "Hilbert's sixth problem: derivation of fluid equations via Boltzmann's theory" Some view a new paper on fluid equations as solid work, but debate its impact, as similar methods are already in many te [bsky, 0 points, 0 comments]
- Hilbert's sixth problem: derivation of fluid equations via Boltzmann's theory [bsky, 0 points, 0 comments]
- Hilbert's sixth problem: derivation of fluid equations via Boltzmann's theory #HackerNews https://arxiv.org/abs/2503.01800 [bsky, 0 points, 0 comments]
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