Researched
Fluid Equations from Atoms
Deng, Hani and Ma derived Boltzmann's gas equation from hard-sphere dynamics for arbitrarily long times, a main step in Hilbert's sixth problem.
Open in the interactive tree →Lanford's 1975 theorem covered only a short time; Yu Deng, Zaher Hani and Xiao Ma (preprint August 2024, accepted by Annals of Mathematics in October 2025) extended it to any time for which the Boltzmann solution stays regular. The Clay Institute calls it a solved part of Hilbert's problem, and Deng's July 2026 Fields Medal cites the derivation for rarefied gases.
Prerequisites
Unlocks
- Navier-Stokes ProblemopenDerives fluid equations from particles, but does not show their solutions stay smooth