平面内波尔兹曼方程的静止解

IF 0.9 4区数学 Q3 MATHEMATICS, APPLIED

Quarterly of Applied Mathematics Pub Date : 2024-03-25 DOI:10.1090/qam/1692

L. Arkeryd, A. Nouri

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引用次数: 0

摘要

论文证明了在 R 2 \mathbb {R}^2 的有界集合中，对于给定的 indata、硬力和碰撞内核中的截断，小速度和接近平行碰撞速度的玻尔兹曼方程静止解的存在性。它不使用任何速度平均法。取而代之的是，它基于离散速度静止情况下的稳定性技术，采用了柯尔莫哥洛夫-里兹-弗雷谢定理，在离散速度静止情况下，速度平均定理是无效的。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Stationary solutions to the Boltzmann equation in the plane

The paper proves existence of stationary solutions to the Boltzmann equation in a bounded set of R 2 \mathbb {R}^2 for given indata, hard forces and truncation in the collision kernel for small velocities and close to parallel colliding velocities. It does not use any averaging in velocity lemma. Instead, it is based on stability techniques employing the Kolmogorov-Riesz-Fréchet theorem, from the discrete velocity stationary case, where the averaging in velocity lemmas are not valid.

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来源期刊

Quarterly of Applied Mathematics 数学-应用数学

CiteScore

1.90

自引率

12.50%

发文量

审稿时长

>12 weeks

期刊介绍： The Quarterly of Applied Mathematics contains original papers in applied mathematics which have a close connection with applications. An author index appears in the last issue of each volume. This journal, published quarterly by Brown University with articles electronically published individually before appearing in an issue, is distributed by the American Mathematical Society (AMS). In order to take advantage of some features offered for this journal, users will occasionally be linked to pages on the AMS website.