平面上的离散速度Boltzmann方程：稳态解
偏微分方程分析
2023-10-25 v1 数学物理
math.MP
摘要
本文证明了法向离散速度Boltzmann方程在平面上、无共线相互作用速度对且给定入射边界值时温和解的存在性。一个关键性质是一列近似的积分碰撞频率的L1紧性。这使用Kolmogorov-Riesz定理证明，此处该定理替代了速度平均的L1紧性——当速度为离散时此紧性不可用。
引用
@article{arxiv.2112.08640,
title = {Discrete velocity Boltzmann equation in the plane: stationary solutions},
author = {Leif Arkeryd and Anne Nouri},
journal= {arXiv preprint arXiv:2112.08640},
year = {2023}
}
备注
The velocity conditions are more general than in the previous version. The end of proof, Section 4, is changed. The appendix is replaced with a reference to the paper where those background properties were first proved. arXiv admin note: substantial text overlap with arXiv:2101.11922, arXiv:2007.02094