有界平面域中稳定驻点涡周围涡度的长时间约束

IF 1.8 1区数学 Q1 MATHEMATICS, APPLIED

Annales De L Institut Henri Poincare-Analyse Non Lineaire Pub Date : 2021-09-01 DOI:10.1016/j.anihpc.2020.11.009

Martin Donati, Dragoș Iftimie

{"title":"有界平面域中稳定驻点涡周围涡度的长时间约束","authors":"Martin Donati, Dragoș Iftimie","doi":"10.1016/j.anihpc.2020.11.009","DOIUrl":null,"url":null,"abstract":"<div>In this paper we consider the incompressible Euler equation in a simply-connected bounded planar domain. We study the confinement of the vorticity around a stationary point vortex. We show that the power law confinement around the center of the unit disk obtained in [2] remains true in the case of a stationary point vortex in a simply-connected bounded domain. The domain and the stationary point vortex must satisfy a condition expressed in terms of the conformal mapping from the domain to the unit disk. Explicit examples are discussed at the end.</div>","PeriodicalId":55514,"journal":{"name":"Annales De L Institut Henri Poincare-Analyse Non Lineaire","volume":"38 5","pages":"Pages 1461-1485"},"PeriodicalIF":1.8000,"publicationDate":"2021-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.anihpc.2020.11.009","citationCount":"6","resultStr":"{\"title\":\"Long time confinement of vorticity around a stable stationary point vortex in a bounded planar domain\",\"authors\":\"Martin Donati, Dragoș Iftimie\",\"doi\":\"10.1016/j.anihpc.2020.11.009\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div>In this paper we consider the incompressible Euler equation in a simply-connected bounded planar domain. We study the confinement of the vorticity around a stationary point vortex. We show that the power law confinement around the center of the unit disk obtained in [2] remains true in the case of a stationary point vortex in a simply-connected bounded domain. The domain and the stationary point vortex must satisfy a condition expressed in terms of the conformal mapping from the domain to the unit disk. Explicit examples are discussed at the end.</div>\",\"PeriodicalId\":55514,\"journal\":{\"name\":\"Annales De L Institut Henri Poincare-Analyse Non Lineaire\",\"volume\":\"38 5\",\"pages\":\"Pages 1461-1485\"},\"PeriodicalIF\":1.8000,\"publicationDate\":\"2021-09-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1016/j.anihpc.2020.11.009\",\"citationCount\":\"6\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Annales De L Institut Henri Poincare-Analyse Non Lineaire\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0294144920301207\",\"RegionNum\":1,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Annales De L Institut Henri Poincare-Analyse Non Lineaire","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0294144920301207","RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}

引用次数: 6

摘要

在本文中，我们考虑了简单连通有界平面域中的不可压缩欧拉方程。我们研究了驻点涡周围的涡度约束。我们证明了在[2]中获得的单位圆盘中心周围的幂律约束在单连通有界域中的驻点涡旋的情况下仍然成立。域和驻点涡必须满足用从域到单位圆盘的保角映射表示的条件。最后讨论了显式例子。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Long time confinement of vorticity around a stable stationary point vortex in a bounded planar domain

In this paper we consider the incompressible Euler equation in a simply-connected bounded planar domain. We study the confinement of the vorticity around a stationary point vortex. We show that the power law confinement around the center of the unit disk obtained in [2] remains true in the case of a stationary point vortex in a simply-connected bounded domain. The domain and the stationary point vortex must satisfy a condition expressed in terms of the conformal mapping from the domain to the unit disk. Explicit examples are discussed at the end.

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

Annales De L Institut Henri Poincare-Analyse Non Lineaire 数学-应用数学

CiteScore

4.10

自引率

5.30%

发文量

审稿时长

>12 weeks

期刊介绍： The Nonlinear Analysis section of the Annales de l''Institut Henri Poincaré is an international journal created in 1983 which publishes original and high quality research articles. It concentrates on all domains concerned with nonlinear analysis, specially applicable to PDE, mechanics, physics, economy, without overlooking the numerical aspects.