On the stability of self-similar blow-up for $C^{1,\alpha}$ solutions to the incompressible Euler equations on $\mathbb{R}^3$

IF 1.8 2区 数学 Q1 MATHEMATICS
T. Elgindi, T. Ghoul, N. Masmoudi
{"title":"On the stability of self-similar blow-up for $C^{1,\\alpha}$ solutions to the incompressible Euler equations on $\\mathbb{R}^3$","authors":"T. Elgindi, T. Ghoul, N. Masmoudi","doi":"10.4310/cjm.2021.v9.n4.a4","DOIUrl":null,"url":null,"abstract":"We study the stability of recently constructed self-similar blow-up solutions to the incompressible Euler equation. A consequence of our work is the existence of finite-energy $C^{1,\\alpha}$ solutions that become singular in finite time in a locally self-similar manner. As a corollary, we also observe that the Beale-Kato-Majda criterion cannot be improved in the class of $C^{1,\\alpha}$ solutions.","PeriodicalId":48573,"journal":{"name":"Cambridge Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":1.8000,"publicationDate":"2019-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"20","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Cambridge Journal of Mathematics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.4310/cjm.2021.v9.n4.a4","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 20

Abstract

We study the stability of recently constructed self-similar blow-up solutions to the incompressible Euler equation. A consequence of our work is the existence of finite-energy $C^{1,\alpha}$ solutions that become singular in finite time in a locally self-similar manner. As a corollary, we also observe that the Beale-Kato-Majda criterion cannot be improved in the class of $C^{1,\alpha}$ solutions.
关于$\mathbb{R}^3$上不可压缩欧拉方程$C^{1, $ α}$解的自相似爆破的稳定性
我们研究了不可压缩欧拉方程最近构造的自相似爆破解的稳定性。我们工作的一个结果是有限能量$C^{1,\alpha}$解的存在性,这些解在有限时间内以局部自相似的方式变得奇异。作为推论,我们还观察到Beale Kato-Majda准则在$C^{1,\alpha}$解的类中不能改进。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
求助全文
约1分钟内获得全文 求助全文
来源期刊
CiteScore
3.10
自引率
0.00%
发文量
7
×
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
确定
请完成安全验证×
copy
已复制链接
快去分享给好友吧!
我知道了
右上角分享
点击右上角分享
0
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 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术官方微信