Javier G'omez-Serrano, Jaemin Park, Jia Shi, Yao Yao
{"title":"Remarks on stationary and uniformly rotating vortex sheets: flexibility results","authors":"Javier G'omez-Serrano, Jaemin Park, Jia Shi, Yao Yao","doi":"10.1098/rsta.2021.0045","DOIUrl":null,"url":null,"abstract":"In this paper, we construct new, uniformly rotating solutions of the vortex sheet equation bifurcating from circles with constant vorticity amplitude. The proof is accomplished via a Lyapunov–Schmidt reduction and a second-order expansion of the reduced system. This article is part of the theme issue ‘Mathematical problems in physical fluid dynamics (part 2)’.","PeriodicalId":20020,"journal":{"name":"Philosophical Transactions of the Royal Society A","volume":"28 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2020-12-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"7","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Philosophical Transactions of the Royal Society A","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1098/rsta.2021.0045","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 7
Abstract
In this paper, we construct new, uniformly rotating solutions of the vortex sheet equation bifurcating from circles with constant vorticity amplitude. The proof is accomplished via a Lyapunov–Schmidt reduction and a second-order expansion of the reduced system. This article is part of the theme issue ‘Mathematical problems in physical fluid dynamics (part 2)’.
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