#### Vol. 14, No. 5, 2021

 Recent Issues
 The Journal About the Journal Editorial Board Editors’ Interests Subscriptions Submission Guidelines Submission Form Policies for Authors Ethics Statement ISSN: 1948-206X (e-only) ISSN: 2157-5045 (print) Author Index To Appear Other MSP Journals
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 ${W}^{1,\infty }$ estimates for the $𝜖$-Milne problem with geometric correction. Also, we develop stronger remainder estimates based on an ${L}^{2m}$-${L}^{\infty }$ framework.

##### Keywords
boundary layer, geometric correction, $W^{1,\infty}$ estimates, $L^{2m}$-$L^{\infty}$ framework
##### Mathematical Subject Classification 2010
Primary: 82B40
Secondary: 34E05, 35L65