具有小旋流的Navier-Stokes方程的全局正则轴对称解

IF 1.2 3区 数学 Q2 MATHEMATICS, APPLIED Journal of Mathematical Fluid Mechanics Pub Date : 2023-08-04 DOI:10.1007/s00021-023-00793-9
Bernard Nowakowski, Wojciech M. Zajaczkowski
{"title":"具有小旋流的Navier-Stokes方程的全局正则轴对称解","authors":"Bernard Nowakowski,&nbsp;Wojciech M. Zajaczkowski","doi":"10.1007/s00021-023-00793-9","DOIUrl":null,"url":null,"abstract":"<div><p>Axially symmetric solutions to the Navier–Stokes equations in a bounded cylinder are considered. On the boundary the normal component of the velocity and the angular components of the velocity and vorticity are assumed to vanish. If the norm of the initial swirl is sufficiently small, then the regularity of axially symmetric, weak solutions is shown. The key tool is a new estimate for the stream function in certain weighted Sobolev spaces.\n</p></div>","PeriodicalId":649,"journal":{"name":"Journal of Mathematical Fluid Mechanics","volume":"25 3","pages":""},"PeriodicalIF":1.2000,"publicationDate":"2023-08-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00021-023-00793-9.pdf","citationCount":"0","resultStr":"{\"title\":\"Global Regular Axially-Symmetric Solutions to the Navier–Stokes Equations with Small Swirl\",\"authors\":\"Bernard Nowakowski,&nbsp;Wojciech M. Zajaczkowski\",\"doi\":\"10.1007/s00021-023-00793-9\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>Axially symmetric solutions to the Navier–Stokes equations in a bounded cylinder are considered. On the boundary the normal component of the velocity and the angular components of the velocity and vorticity are assumed to vanish. If the norm of the initial swirl is sufficiently small, then the regularity of axially symmetric, weak solutions is shown. The key tool is a new estimate for the stream function in certain weighted Sobolev spaces.\\n</p></div>\",\"PeriodicalId\":649,\"journal\":{\"name\":\"Journal of Mathematical Fluid Mechanics\",\"volume\":\"25 3\",\"pages\":\"\"},\"PeriodicalIF\":1.2000,\"publicationDate\":\"2023-08-04\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://link.springer.com/content/pdf/10.1007/s00021-023-00793-9.pdf\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Mathematical Fluid Mechanics\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s00021-023-00793-9\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Mathematical Fluid Mechanics","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s00021-023-00793-9","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0

摘要

研究了有界圆柱体中Navier-Stokes方程的轴对称解。在边界上,假设速度的法向分量和速度和涡量的角分量消失。如果初始旋流范数足够小,则显示出轴对称弱解的规律性。关键工具是对某些加权Sobolev空间中的流函数进行新的估计。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
查看原文
分享 分享
微信好友 朋友圈 QQ好友 复制链接
本刊更多论文
Global Regular Axially-Symmetric Solutions to the Navier–Stokes Equations with Small Swirl

Axially symmetric solutions to the Navier–Stokes equations in a bounded cylinder are considered. On the boundary the normal component of the velocity and the angular components of the velocity and vorticity are assumed to vanish. If the norm of the initial swirl is sufficiently small, then the regularity of axially symmetric, weak solutions is shown. The key tool is a new estimate for the stream function in certain weighted Sobolev spaces.

求助全文
通过发布文献求助,成功后即可免费获取论文全文。 去求助
来源期刊
CiteScore
2.00
自引率
15.40%
发文量
97
审稿时长
>12 weeks
期刊介绍: The Journal of Mathematical Fluid Mechanics (JMFM)is a forum for the publication of high-quality peer-reviewed papers on the mathematical theory of fluid mechanics, with special regards to the Navier-Stokes equations. As an important part of that, the journal encourages papers dealing with mathematical aspects of computational theory, as well as with applications in science and engineering. The journal also publishes in related areas of mathematics that have a direct bearing on the mathematical theory of fluid mechanics. All papers will be characterized by originality and mathematical rigor. For a paper to be accepted, it is not enough that it contains original results. In fact, results should be highly relevant to the mathematical theory of fluid mechanics, and meet a wide readership.
期刊最新文献
\(L^{r}\)-Results of the Stationary Navier–Stokes Equations with Nonzero Velocity at Infinity Partial Regularity for Navier-Stokes Equations Homogenization of Non-Homogeneous Incompressible Navier–Stokes System in Critically Perforated Domains On Rough Calderón Solutions to the Navier–Stokes Equations and Applications to the Singular Set The Navier–Stokes Cauchy Problem in a Class of Weighted Function Spaces
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
现在去查看 取消
×
提示
确定
0
微信
客服QQ
Book学术公众号 扫码关注我们
反馈
×
意见反馈
请填写您的意见或建议
请填写您的手机或邮箱
已复制链接
已复制链接
快去分享给好友吧!
我知道了
×
扫码分享
扫码分享
Book学术官方微信
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术
文献互助 智能选刊 最新文献 互助须知 联系我们:info@booksci.cn
Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。
Copyright © 2023 Book学术 All rights reserved.
ghs 京公网安备 11010802042870号 京ICP备2023020795号-1