Derivation of hydrodynamic limit from Knudsen gas model

Abstract

We prove that the solutions of the kinetic equation modelling the reflection of particles according to a reversible law and considered on the $n$-torus converge to the diffusion equation when the main free path goes to zero. This extends the work of Bardos, Golse and Colonna [2] to the case of any $n$-dimensional torus ergodic automorphism.