{"title":"关于Sadovskii涡片的存在性：对称反旋转均匀涡的接触对","authors":"Kyudong Choi, In-Jee Jeong, Young-Jin Sim","doi":"10.1007/s40818-025-00212-4","DOIUrl":null,"url":null,"abstract":"<div><p>The Sadovskii vortex patch is a traveling wave for the two-dimensional incompressible Euler equations consisting of an odd symmetric pair of vortex patches touching the symmetry axis. Its existence was first suggested by numerical computations of Sadovskii in [J. Appl. Math. Mech., 1971], and has gained significant interest due to its relevance in inviscid limit of planar flows via Prandtl–Batchelor theory and as the asymptotic state for vortex ring dynamics. In this work, we prove the existence of a Sadovskii vortex patch, by solving the energy maximization problem under the exact impulse condition and an upper bound on the circulation.</p></div>","PeriodicalId":36382,"journal":{"name":"Annals of Pde","volume":"11 2","pages":""},"PeriodicalIF":2.6000,"publicationDate":"2025-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s40818-025-00212-4.pdf","citationCount":"0","resultStr":"{\"title\":\"On Existence of Sadovskii Vortex Patch: A Touching Pair of Symmetric Counter-Rotating Uniform Vortices\",\"authors\":\"Kyudong Choi, In-Jee Jeong, Young-Jin Sim\",\"doi\":\"10.1007/s40818-025-00212-4\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>The Sadovskii vortex patch is a traveling wave for the two-dimensional incompressible Euler equations consisting of an odd symmetric pair of vortex patches touching the symmetry axis. Its existence was first suggested by numerical computations of Sadovskii in [J. Appl. Math. Mech., 1971], and has gained significant interest due to its relevance in inviscid limit of planar flows via Prandtl–Batchelor theory and as the asymptotic state for vortex ring dynamics. In this work, we prove the existence of a Sadovskii vortex patch, by solving the energy maximization problem under the exact impulse condition and an upper bound on the circulation.</p></div>\",\"PeriodicalId\":36382,\"journal\":{\"name\":\"Annals of Pde\",\"volume\":\"11 2\",\"pages\":\"\"},\"PeriodicalIF\":2.6000,\"publicationDate\":\"2025-07-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://link.springer.com/content/pdf/10.1007/s40818-025-00212-4.pdf\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Annals of Pde\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s40818-025-00212-4\",\"RegionNum\":1,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Annals of Pde","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s40818-025-00212-4","RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
On Existence of Sadovskii Vortex Patch: A Touching Pair of Symmetric Counter-Rotating Uniform Vortices
The Sadovskii vortex patch is a traveling wave for the two-dimensional incompressible Euler equations consisting of an odd symmetric pair of vortex patches touching the symmetry axis. Its existence was first suggested by numerical computations of Sadovskii in [J. Appl. Math. Mech., 1971], and has gained significant interest due to its relevance in inviscid limit of planar flows via Prandtl–Batchelor theory and as the asymptotic state for vortex ring dynamics. In this work, we prove the existence of a Sadovskii vortex patch, by solving the energy maximization problem under the exact impulse condition and an upper bound on the circulation.
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