Deriving Fluid Equations from Kinetic Theory

The authors rigorously derive the compressible Euler and incompressible Navier-Stokes-Fourier equations from Newton’s laws via Boltzmann’s kinetic theory.

They base their proof on a hard sphere particle system undergoing elastic collisions to connect microscopic dynamics to fluid equations.

They extend earlier work by deriving Boltzmann’s equation on two- and three-dimensional tori.

This result provides a resolution to Hilbert’s sixth problem on deriving fluid mechanics laws from kinetic theory.