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arXiv · 2304.08800

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

I-Kun Chen·Ping-Han Chuang·Chun-Hsiung Hsia·Daisuke Kawagoe·Jhe-Kuan Su
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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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I-Kun Chen, Ping-Han Chuang, Chun-Hsiung Hsia, Daisuke Kawagoe, Jhe-Kuan Su. 2023-04-18. On the Existence of $H^1$ solutions for Stationary Linearized Boltzmann Equations in a Small Convex Domain. https://arxiv.org/abs/2304.08800

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