Deriving Fluid Equations via Boltzmann Theory

The paper rigorously derives fundamental fluid mechanics equations, including the compressible Euler and incompressible Navier-Stokes-Fourier equations, from a microscopic hard sphere particle model undergoing elastic collisions.

It resolves Hilbert’s sixth problem by completing the program of deriving macroscopic fluid equations from Newton’s laws using Boltzmann’s kinetic theory.

The proof builds on and extends previous work by deriving Boltzmann’s equation on two- and three-dimensional tori.