On the Existence of H¹ solutions for Stationary Linearized Boltzmann Equations in a Small Convex Domain

2023/04/18 by Chen, I-Kun, Chuang, Ping-Han, Hsia, Chun-Hsiung +2
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2304.08800

Abstract

In this article, we investigate the incoming boundary value problem for the stationary linearized Boltzmann equations in Ω⊆ ℝ³. For a C² bounded domain with boundary of positive Gaussian curvature, the existence theory is established in H¹(Ω× ℝ³) provided that the diameter of the domain Ω is small enough.

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