Rigorous derivation of the generalized Reynolds equation from the Boltzmann equation
Analysis of PDEs
2020-02-12 v1
Abstract
We study the stationary Boltzmann equation in a thin slab for a rarefied gas for which the molecular mean free path is comparable to the film thickness. We prove that there exists a solution which converges, in the hydrodynamic limit, to a density Maxwellian -- this density is obtained as the solution to the generalized Reynolds equation. The convergence is proved using a truncated Hilbert expansion by carefully estimating the remainder.
Keywords
Cite
@article{arxiv.2002.04093,
title = {Rigorous derivation of the generalized Reynolds equation from the Boltzmann equation},
author = {Andrei Ichim},
journal= {arXiv preprint arXiv:2002.04093},
year = {2020}
}