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On the Existence of $H^1$ solutions for Stationary Linearized Boltzmann Equations in a Small Convex Domain

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arxiv 2304.08800 v1 pith:AC7OGHZ3 submitted 2023-04-18 math.AP

I-Kun Chen , Ping-Han Chuang , Chun-Hsiung Hsia , Daisuke Kawagoe , Jhe-Kuan Su This is my paper · ORCID
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keywords domainomegaboltzmannboundaryequationsexistencelinearizedmathbb
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abstract

In this article, we investigate the incoming boundary value problem for the stationary linearized Boltzmann equations in $ \Omega \subseteq \mathbb{R}^{3}$. For a $C^2$ bounded domain with boundary of positive Gaussian curvature, the existence theory is established in $H^{1}(\Omega \times \mathbb{R}^{3})$ provided that the diameter of the domain $\Omega$ is small enough.

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  1. On existence of spatially regular strong solutions for a class of transport equations

    math.AP 2025-04 conditional novelty 5.0 of 10

    For linear Boltzmann transport problems whose data vanish on the inflow and characteristic boundary parts, strong solutions exist with arbitrary spatial Sobolev regularity, including with a continuous slowing-down ene...

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