{"title":"点涡二维水波Rayleigh-Taylor不稳定性的跃迁","authors":"Qingtang Su","doi":"10.1007/s40818-023-00157-6","DOIUrl":null,"url":null,"abstract":"<div><p>In this paper, by considering 2d water waves with a pair of point vortices, we prove the existence of water waves with sign-changing Taylor sign coefficients. That is, the strong Taylor sign condition holds initially, while it breaks down at a later time. Such a phenomenon can be regarded as the transition between the stable and unstable regime in the sense of Rayleigh-Taylor of water waves. As a byproduct, we prove the wellposedness of 2d water waves in Gevrey-2 spaces.</p></div>","PeriodicalId":36382,"journal":{"name":"Annals of Pde","volume":"9 2","pages":""},"PeriodicalIF":2.4000,"publicationDate":"2023-10-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s40818-023-00157-6.pdf","citationCount":"1","resultStr":"{\"title\":\"On the Transition of the Rayleigh-Taylor Instability in 2d Water Waves with Point Vortices\",\"authors\":\"Qingtang Su\",\"doi\":\"10.1007/s40818-023-00157-6\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>In this paper, by considering 2d water waves with a pair of point vortices, we prove the existence of water waves with sign-changing Taylor sign coefficients. That is, the strong Taylor sign condition holds initially, while it breaks down at a later time. Such a phenomenon can be regarded as the transition between the stable and unstable regime in the sense of Rayleigh-Taylor of water waves. As a byproduct, we prove the wellposedness of 2d water waves in Gevrey-2 spaces.</p></div>\",\"PeriodicalId\":36382,\"journal\":{\"name\":\"Annals of Pde\",\"volume\":\"9 2\",\"pages\":\"\"},\"PeriodicalIF\":2.4000,\"publicationDate\":\"2023-10-17\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://link.springer.com/content/pdf/10.1007/s40818-023-00157-6.pdf\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Annals of Pde\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s40818-023-00157-6\",\"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/s40818-023-00157-6","RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
On the Transition of the Rayleigh-Taylor Instability in 2d Water Waves with Point Vortices
In this paper, by considering 2d water waves with a pair of point vortices, we prove the existence of water waves with sign-changing Taylor sign coefficients. That is, the strong Taylor sign condition holds initially, while it breaks down at a later time. Such a phenomenon can be regarded as the transition between the stable and unstable regime in the sense of Rayleigh-Taylor of water waves. As a byproduct, we prove the wellposedness of 2d water waves in Gevrey-2 spaces.
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