Hilbert's sixth problem: derivation of fluid equations via Boltzmann's kinetic theory
Analysis of PDEs
2025-03-04 v1 Mathematical Physics
math.MP
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).
Cite
@article{arxiv.2503.01800,
title = {Hilbert's sixth problem: derivation of fluid equations via Boltzmann's kinetic theory},
author = {Yu Deng and Zaher Hani and Xiao Ma},
journal= {arXiv preprint arXiv:2503.01800},
year = {2025}
}
Comments
48 pages, 5 figures. arXiv admin note: text overlap with arXiv:2408.07818