Daomin Cao, Guolin Qin, Weicheng Zhan, Changjun Zou
{"title":"Uniqueness and stability of traveling vortex pairs for the incompressible Euler equation","authors":"Daomin Cao, Guolin Qin, Weicheng Zhan, Changjun Zou","doi":"10.1007/s40818-024-00191-y","DOIUrl":null,"url":null,"abstract":"<div><p>In this paper, we establish the uniqueness and nonlinear stability of concentrated symmetric traveling vortex patch-pairs for the 2D Euler equation. We also prove the uniqueness of concentrated rotating polygons as well. The proofs are achieved by a combination of the local Pohozaev identity, a detailed description of asymptotic behaviors of the solutions and some symmetry properties obtained by the method of moving planes.</p></div>","PeriodicalId":36382,"journal":{"name":"Annals of Pde","volume":"11 1","pages":""},"PeriodicalIF":2.4000,"publicationDate":"2024-12-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Annals of Pde","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s40818-024-00191-y","RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
Uniqueness and stability of traveling vortex pairs for the incompressible Euler equation
In this paper, we establish the uniqueness and nonlinear stability of concentrated symmetric traveling vortex patch-pairs for the 2D Euler equation. We also prove the uniqueness of concentrated rotating polygons as well. The proofs are achieved by a combination of the local Pohozaev identity, a detailed description of asymptotic behaviors of the solutions and some symmetry properties obtained by the method of moving planes.
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