Regularity for diffuse reflection boundary problem to the stationary linearized Boltzmann equation in a convex domain

2018/03/11 by I‐Kun Chen, Chen, I-Kun, Chun-Hsiung Hsia +3 · 2 citations
Engineering · Mathematics · #Analysis of PDEs (math.AP) #Composite Material Mechanics #FOS: Mathematics #Gas Dynamics and Kinetic Theory #Numerical methods in inverse problems

paper · pdf · doi:10.48550/arxiv.1803.03985

openalex publication_date 2018/03/11 · openalex created_date 2018/03/29 · openalex updated_date 2026/07/28

Abstract

We investigate the regularity issue for the diffuse reflection boundary problem to the stationary linearized Boltzmann equation for hard sphere potential, cutoff hard potential, or cutoff Maxwellian molecular gases in a strictly convex bounded domain. We obtain pointwise estimates for first derivatives of the solution provided the boundary temperature is bounded differentiable and the solution is bounded. This result can be understood as a stationary version of the velocity averaging lemma and mixture lemma.

Cited by

• Steady Solutions to the Relativistic Boltzmann Equation in a Slab
• Optimal C^(1)/(2) regularity of the Boltzmann equation in non-convex domains

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