From the Boltzmann Equation to the Euler Equations in the Presence of Boundaries

TL;DR

This paper investigates the derivation of Euler equations from the Boltzmann equation in bounded domains, extending previous results to more general boundary conditions beyond Maxwell's accommodation.

Contribution

It extends recent mathematical results on the fluid dynamic limit of the Boltzmann equation to broader boundary conditions, enhancing understanding of boundary effects.

Findings

Established convergence of Boltzmann to Euler equations with general boundary conditions

Extended mathematical framework for boundary conditions in kinetic-fluid limits

Provided rigorous analysis of boundary effects in fluid dynamic limits

Abstract

The fluid dynamic limit of the Boltzmann equation leading to the Euler equations for an incompressible fluid with constant density in the presence of material boundaries shares some important features with the better known inviscid limit of the Navier-Stokes equations. The present paper slightly extends recent results from [C. Bardos, F. Golse, L. Paillard, Comm. Math. Sci., 10 (2012), 159--190] to the case of boundary conditions for the Boltzmann equation more general than Maxwell's accomodation condition.