{"title":"On an Oberbeck-Boussinesq model relating to the motion of a viscous fluid subject to heating","authors":"Angela Iannelli","doi":"10.1515/math-2024-0032","DOIUrl":null,"url":null,"abstract":"This article surveys some results in the study of Iannelli [<jats:italic>Su un modello di Oberbeck-Boussinesq relativo al moto di un fluido viscoso soggetto a riscaldamento</jats:italic>, Fisica Matematica, Istituto Lombardo (rend. Sc.) A 121 (1987), 145–191], in which the motion of a viscous, compressible fluid in a two-dimensional domain, subject to heating at the walls, is studied. A global existence and uniqueness theorem for the time-dependent problem is given, and also, under more stringent assumptions, an existence and uniqueness theorem in the stationary case is given. A theorem on the asymptotic behavior for <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_math-2024-0032_eq_001.png\"/> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mi>t</m:mi> <m:mo>→</m:mo> <m:mi>∞</m:mi> </m:math> <jats:tex-math>t\\to \\infty </jats:tex-math> </jats:alternatives> </jats:inline-formula> of the time-dependent solutions is proved.","PeriodicalId":48713,"journal":{"name":"Open Mathematics","volume":null,"pages":null},"PeriodicalIF":1.0000,"publicationDate":"2024-08-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Open Mathematics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1515/math-2024-0032","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
This article surveys some results in the study of Iannelli [Su un modello di Oberbeck-Boussinesq relativo al moto di un fluido viscoso soggetto a riscaldamento, Fisica Matematica, Istituto Lombardo (rend. Sc.) A 121 (1987), 145–191], in which the motion of a viscous, compressible fluid in a two-dimensional domain, subject to heating at the walls, is studied. A global existence and uniqueness theorem for the time-dependent problem is given, and also, under more stringent assumptions, an existence and uniqueness theorem in the stationary case is given. A theorem on the asymptotic behavior for t→∞t\to \infty of the time-dependent solutions is proved.
本文概述了 Iannelli [Su un modello di Oberbeck-Boussinesq relativo al moto di un fluido viscoso soggetto a riscaldamento, Fisica Matematica, Istituto Lombardo (rend. Sc.) A 121 (1987), 145-191] 的研究中的一些结果，其中研究了粘性可压缩流体在二维域中受壁面加热影响的运动。给出了时变问题的全局存在性和唯一性定理，并在更严格的假设条件下给出了静止情况下的存在性和唯一性定理。证明了时变解在 t → ∞ t\to \infty 时的渐近行为定理。
期刊介绍：
Open Mathematics - formerly Central European Journal of Mathematics
Open Mathematics is a fully peer-reviewed, open access, electronic journal that publishes significant, original and relevant works in all areas of mathematics. The journal provides the readers with free, instant, and permanent access to all content worldwide; and the authors with extensive promotion of published articles, long-time preservation, language-correction services, no space constraints and immediate publication.
Open Mathematics is listed in Thomson Reuters - Current Contents/Physical, Chemical and Earth Sciences. Our standard policy requires each paper to be reviewed by at least two Referees and the peer-review process is single-blind.
Aims and Scope
The journal aims at presenting high-impact and relevant research on topics across the full span of mathematics. Coverage includes:
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