Hilbert's Sixth Problem: Derivation of the Boltzmann and Fluid Equations

This lecture by Yu Deng from the University of Chicago Department of Mathematics presents recent research conducted with Zaher Hani and Xiao Ma on deriving the Boltzmann equation from hard sphere dynamics in the Boltzmann-Grad limit. Learn about their breakthrough work that covers the full time range in which strong solutions to the Boltzmann equation exist, both in Euclidean settings (for dimensions ≥ 2) and periodic settings (for dimensions 2 and 3). Discover how this research resolves Hilbert's Sixth Problem regarding the derivation of hydrodynamic equations from colliding particle systems, using the Boltzmann equation as an intermediate step. The presentation also demonstrates how the corresponding fluid equations can be derived from hard sphere dynamics as a corollary of their main results.