{"title":"Stationary solutions to the Boltzmann equation in the plane","authors":"L. Arkeryd, A. Nouri","doi":"10.1090/qam/1692","DOIUrl":null,"url":null,"abstract":"The paper proves existence of stationary solutions to the Boltzmann equation in a bounded set of \n\n \n \n \n R\n \n 2\n \n \\mathbb {R}^2\n \n\n 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.","PeriodicalId":20964,"journal":{"name":"Quarterly of Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":0.9000,"publicationDate":"2024-03-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Quarterly of Applied Mathematics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1090/qam/1692","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
Abstract
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.
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.