二维不可压缩类欧拉方程的稳定性和衰减

IF 1.2 3区 数学 Q2 MATHEMATICS, APPLIED Journal of Mathematical Fluid Mechanics Pub Date : 2023-10-11 DOI:10.1007/s00021-023-00824-5
Hongxia Lin, Qing Sun, Sen Liu, Heng Zhang
{"title":"二维不可压缩类欧拉方程的稳定性和衰减","authors":"Hongxia Lin,&nbsp;Qing Sun,&nbsp;Sen Liu,&nbsp;Heng Zhang","doi":"10.1007/s00021-023-00824-5","DOIUrl":null,"url":null,"abstract":"<div><p>This paper is concerned with the two-dimensional incompressible Euler-like equations. More precisely, we consider the system with only damping in the vertical component equation. When the domain is the whole space <span>\\(\\mathbb {R}^2\\)</span>, it is well known that solutions of the incompressible Euler equations can grow rapidly in time while solutions of the Euler equations with full damping are stable. As the intermediate case of the two equations, the global well-posedness and the stability in <span>\\(\\mathbb {R}^2\\)</span> remain the outstanding open problem. Our attentions here focus on the domain <span>\\(\\Omega =\\mathbb {T}\\times \\mathbb {R}\\)</span> with <span>\\(\\mathbb {T}\\)</span> being 1D periodic box. Compared with <span>\\(\\mathbb {R}^2\\)</span>, the domain <span>\\(\\Omega \\)</span> allows us to separate the physical quantity <i>f</i> into its horizontal average <span>\\(\\overline{f}\\)</span> and the corresponding oscillation <span>\\(\\widetilde{f}\\)</span>. By deriving the strong Poincaré inequality and two anisotropic inequalities related to <span>\\(\\widetilde{f}\\)</span>, we are able to employ the time-weighted energy estimate to establish the stability of the solution and the precise large-time behavior of the system provided that the initial data is small and satisfies the reflection symmetry condition.</p></div>","PeriodicalId":649,"journal":{"name":"Journal of Mathematical Fluid Mechanics","volume":"25 4","pages":""},"PeriodicalIF":1.2000,"publicationDate":"2023-10-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"The Stability and Decay for the 2D Incompressible Euler-Like Equations\",\"authors\":\"Hongxia Lin,&nbsp;Qing Sun,&nbsp;Sen Liu,&nbsp;Heng Zhang\",\"doi\":\"10.1007/s00021-023-00824-5\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>This paper is concerned with the two-dimensional incompressible Euler-like equations. More precisely, we consider the system with only damping in the vertical component equation. When the domain is the whole space <span>\\\\(\\\\mathbb {R}^2\\\\)</span>, it is well known that solutions of the incompressible Euler equations can grow rapidly in time while solutions of the Euler equations with full damping are stable. As the intermediate case of the two equations, the global well-posedness and the stability in <span>\\\\(\\\\mathbb {R}^2\\\\)</span> remain the outstanding open problem. Our attentions here focus on the domain <span>\\\\(\\\\Omega =\\\\mathbb {T}\\\\times \\\\mathbb {R}\\\\)</span> with <span>\\\\(\\\\mathbb {T}\\\\)</span> being 1D periodic box. Compared with <span>\\\\(\\\\mathbb {R}^2\\\\)</span>, the domain <span>\\\\(\\\\Omega \\\\)</span> allows us to separate the physical quantity <i>f</i> into its horizontal average <span>\\\\(\\\\overline{f}\\\\)</span> and the corresponding oscillation <span>\\\\(\\\\widetilde{f}\\\\)</span>. By deriving the strong Poincaré inequality and two anisotropic inequalities related to <span>\\\\(\\\\widetilde{f}\\\\)</span>, we are able to employ the time-weighted energy estimate to establish the stability of the solution and the precise large-time behavior of the system provided that the initial data is small and satisfies the reflection symmetry condition.</p></div>\",\"PeriodicalId\":649,\"journal\":{\"name\":\"Journal of Mathematical Fluid Mechanics\",\"volume\":\"25 4\",\"pages\":\"\"},\"PeriodicalIF\":1.2000,\"publicationDate\":\"2023-10-11\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Mathematical Fluid Mechanics\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s00021-023-00824-5\",\"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/s00021-023-00824-5","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

本文研究二维不可压缩类欧拉方程。更准确地说,我们考虑在垂直分量方程中只有阻尼的系统。当定义域为整个空间\(\mathbb {R}^2\)时,不可压缩欧拉方程的解在时间上可以快速增长,而具有全阻尼的欧拉方程的解是稳定的。作为两种方程的中间情况,\(\mathbb {R}^2\)方程的全局适定性和稳定性仍然是一个突出的开放性问题。我们的注意力集中在域\(\Omega =\mathbb {T}\times \mathbb {R}\)上,\(\mathbb {T}\)是一维周期框。与\(\mathbb {R}^2\)相比,域\(\Omega \)允许我们将物理量f分离为其水平平均值\(\overline{f}\)和相应的振荡\(\widetilde{f}\)。通过推导强poincar不等式和与\(\widetilde{f}\)相关的两个各向异性不等式,我们可以利用时间加权能量估计来建立解的稳定性和系统在初始数据小且满足反射对称条件下的精确大时间行为。
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
The Stability and Decay for the 2D Incompressible Euler-Like Equations

This paper is concerned with the two-dimensional incompressible Euler-like equations. More precisely, we consider the system with only damping in the vertical component equation. When the domain is the whole space \(\mathbb {R}^2\), it is well known that solutions of the incompressible Euler equations can grow rapidly in time while solutions of the Euler equations with full damping are stable. As the intermediate case of the two equations, the global well-posedness and the stability in \(\mathbb {R}^2\) remain the outstanding open problem. Our attentions here focus on the domain \(\Omega =\mathbb {T}\times \mathbb {R}\) with \(\mathbb {T}\) being 1D periodic box. Compared with \(\mathbb {R}^2\), the domain \(\Omega \) allows us to separate the physical quantity f into its horizontal average \(\overline{f}\) and the corresponding oscillation \(\widetilde{f}\). By deriving the strong Poincaré inequality and two anisotropic inequalities related to \(\widetilde{f}\), we are able to employ the time-weighted energy estimate to establish the stability of the solution and the precise large-time behavior of the system provided that the initial data is small and satisfies the reflection symmetry condition.

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
相关文献
二甲双胍通过HDAC6和FoxO3a转录调控肌肉生长抑制素诱导肌肉萎缩
IF 8.9 1区 医学Journal of Cachexia, Sarcopenia and MusclePub Date : 2021-11-02 DOI: 10.1002/jcsm.12833
Min Ju Kang, Ji Wook Moon, Jung Ok Lee, Ji Hae Kim, Eun Jeong Jung, Su Jin Kim, Joo Yeon Oh, Sang Woo Wu, Pu Reum Lee, Sun Hwa Park, Hyeon Soo Kim
具有疾病敏感单倍型的非亲属供体脐带血移植后的1型糖尿病
IF 3.2 3区 医学Journal of Diabetes InvestigationPub Date : 2022-11-02 DOI: 10.1111/jdi.13939
Kensuke Matsumoto, Taisuke Matsuyama, Ritsu Sumiyoshi, Matsuo Takuji, Tadashi Yamamoto, Ryosuke Shirasaki, Haruko Tashiro
封面:蛋白质组学分析确定IRSp53和fastin是PRV输出和直接细胞-细胞传播的关键
IF 3.4 4区 生物学ProteomicsPub Date : 2019-12-02 DOI: 10.1002/pmic.201970201
Fei-Long Yu, Huan Miao, Jinjin Xia, Fan Jia, Huadong Wang, Fuqiang Xu, Lin Guo
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
The Navier–Stokes Cauchy Problem in a Class of Weighted Function Spaces Sharp Interface Limit for Compressible Immiscible Two-Phase Dynamics with Relaxation Regularity properties of a generalized Oseen evolution operator in exterior domains, with applications to the Navier–Stokes initial value problem Liouville Type Theorems for the Stationary Navier–Stokes Equations in High-Dimension Without Vanishing Condition Grad-Div Stabilized Finite Element Method for Magnetohydrodynamic Flows at Low Magnetic Reynolds Numbers
×
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