Regularity of Stationary Boltzmann equation in Convex Domains

2020/06/16 by Hongxu Chen, Chanwoo Kim, Chen, Hongxu +1 · 3 citations
Computer Science · Engineering · Mathematics · Physics and Astronomy · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Composite Material Mechanics #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Numerical methods in inverse problems #math-ph #math.AP #math.MP

paper · pdf · doi:10.48550/arxiv.2006.09279

78 pages, some presentation improvement

openalex publication_date 2020/06/16 · arxiv created 2021/03/26 · arxiv updated 2021/03/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Higher regularity estimate has been a challenging question for the Boltzmann equation in bounded domains. Indeed, it is well-known to have "the non-existence of a second order derivative at the boundary" in [15] even for symmetric convex domains such as a disk or sphere. In this paper we answer this question in the affirmative by constructing the C^1,β solutions away from the grazing boundary, for any β<1, to the stationary Boltzmann equation with the non-isothermal diffuse boundary condition in strictly convex domains, as long as a smooth wall temperature has small fluctuation pointwisely.

Cited by

• Steady Solutions to the Relativistic Boltzmann Equation in a Slab
• The Boltzmann equation in an infinite layer: spectrum and asymptotics toward the heat equation
• Optimal C^(1)/(2) regularity of the Boltzmann equation in non-convex domains

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