HackerPapers

arXiv:2503.01800math.AP

Hilbert's sixth problem: derivation of fluid equations via Boltzmann's kinetic theory

Yu Deng, Zaher Hani, Xiao Ma

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).

arXiv comments
48 pages, 5 figures. arXiv admin note: text overlap with arXiv:2408.07818
Journal reference
DOI
Subjects
math.APAnalysis of PDEs math-phMathematical Physics

On Hacker News

Linked by 2 identifiable commenters in 2 comments across 2 threads, from Apr 2025 to Apr 2025. Found in 5 HN submissions from Mar 2025 to Jul 2025. Open submission discussions.

Comments linking this paper, per year.

Discussed in comments2 threads

  1. Mathematicians just solved a 125-year-old problem, uniting 3 theories in physics 1 comment
  2. Chinese mathematicans in US say they cracked century-old fluid mechanics puzzle 1 comment

    • https://arxiv.org/abs/2503.01800 This is the preprint in question. I haven’t reviewed it rigorously, but I’m a mathematician in a vaguely related domain and the proof outline seems plausible to me. Prior work in https://arxiv.org/pdf/2408.07818 claims to prove that Boltzmann’s…

      TimorousBestieView on HNParent context

Submitted to Hacker News

Connected through shared HN threads, not inferred similarity or a recommendation.