Vol. 14, No. 5, 2021

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

Lei Wu

Vol. 14 (2021), No. 5, 1363–1428
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 W1, estimates for the 𝜖-Milne problem with geometric correction. Also, we develop stronger remainder estimates based on an L2m-L 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