On the Existence and Regularity for Stationary Boltzmann Equation in a Small Domain

I-Kun Chen; Chun-Hsiung Hsia; Daisuke Kawagoe; Jhe-Kuan Su

On the Existence and Regularity for Stationary Boltzmann Equation in a Small Domain

Analysis of PDEs 2024-03-20 v2

Authors: I-Kun Chen , Chun-Hsiung Hsia , Daisuke Kawagoe , Jhe-Kuan Su

Abstract

In this article, we study the stationary Boltzmann equation with the incoming boundary condition for the hard potential cases. Assuming the smallness of the domain and a suitable normal curvature condition on the boundary, we find a suitable solution space which is a proper subset of the $W^{1,p}$ space for $1 \leq p <3$ .

Keywords

stationary Boltzmann equation incoming boundary condition hard potential small domain normal curvature existence regularity W^{1,p} space

Cite

@article{arxiv.2403.10016,
  title  = {On the Existence and Regularity for Stationary Boltzmann Equation in a Small Domain},
  author = {I-Kun Chen and Chun-Hsiung Hsia and Daisuke Kawagoe and Jhe-Kuan Su},
  journal= {arXiv preprint arXiv:2403.10016},
  year   = {2024}
}

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