Boundary layer of the Boltzmann equation in 2-dimensional convex domains

Wu, Lei

doi:10.2140/apde.2021.14.1363

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Boundary layer of the Boltzmann equation in 2-dimensional convex domains

Lei Wu

Vol. 14 (2021), No. 5, 1363–1428

DOI: 10.2140/apde.2021.14.1363

Abstract

Consider the stationary Boltzmann equation in 2-dimensional convex domains with diffusive boundary condition. We establish the hydrodynamic limits while the boundary layers are present, and derive the steady Navier–Stokes–Fourier system with nonslip boundary conditions. Our contribution focuses on novel weighted $W^{1, \infty}$ estimates for the $𝜖$ -Milne problem with geometric correction. Also, we develop stronger remainder estimates based on an $L^{2 m}$ - $L^{\infty}$ framework.

Keywords

boundary layer, geometric correction, $W^{1,\infty}$ estimates, $L^{2m}$-$L^{\infty}$ framework

Mathematical Subject Classification 2010

Primary: 82B40

Secondary: 34E05, 35L65

Milestones

Received: 24 October 2018

Revised: 14 May 2019

Accepted: 27 January 2020

Published: 22 August 2021

Authors

Lei Wu
Department of Mathematics Lehigh University Bethlehem, PA United States

Vol. 14, No. 5, 2021