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2021 Boundary layer of the Boltzmann equation in 2-dimensional convex domains
Lei Wu
Anal. PDE 14(5): 1363-1428 (2021). 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 W1, estimates for the 𝜖-Milne problem with geometric correction. Also, we develop stronger remainder estimates based on an L2m-L framework.

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Lei Wu. "Boundary layer of the Boltzmann equation in 2-dimensional convex domains." Anal. PDE 14 (5) 1363 - 1428, 2021. https://doi.org/10.2140/apde.2021.14.1363

Information

Received: 24 October 2018; Revised: 14 May 2019; Accepted: 27 January 2020; Published: 2021
First available in Project Euclid: 6 January 2022

Digital Object Identifier: 10.2140/apde.2021.14.1363

Subjects:
Primary: 82B40
Secondary: 34E05 , 35L65

Keywords: boundary layer , geometric correction , L2m-L∞ framework , W1,∞ estimates

Rights: Copyright © 2021 Mathematical Sciences Publishers

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Vol.14 • No. 5 • 2021
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