Rigorous derivation of the generalized Reynolds equation from the Boltzmann equation

Andrei Ichim

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arXiv · 2002.04093

Rigorous derivation of the generalized Reynolds equation from the Boltzmann equation

Andrei Ichim

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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.

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Andrei Ichim. 2020-02-10. Rigorous derivation of the generalized Reynolds equation from the Boltzmann equation. https://arxiv.org/abs/2002.04093

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