{"title":"五阶KdV方程在（H^｛-1｝（\\pmb｛\\mathbb｛R｝）中的全局适定性","authors":"Bjoern Bringmann, Rowan Killip, Monica Visan","doi":"10.1007/s40818-021-00111-4","DOIUrl":null,"url":null,"abstract":"<div><p>We prove global well-posedness of the fifth-order Korteweg-de Vries equation on the real line for initial data in <span>\\(H^{-1}(\\mathbb {R})\\)</span>. Global well-posedness in <span>\\(L^2({\\mathbb {R}})\\)</span> was shown previously in [8] using the method of commuting flows. Since this method is insensitive to the ambient geometry, it cannot go beyond the sharp <span>\\( L^2\\)</span> threshold for the torus demonstrated in [3]. To prove our result, we introduce a new strategy that integrates dispersive effects into the method of commuting flows.</p></div>","PeriodicalId":36382,"journal":{"name":"Annals of Pde","volume":"7 2","pages":""},"PeriodicalIF":2.4000,"publicationDate":"2021-08-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s40818-021-00111-4","citationCount":"7","resultStr":"{\"title\":\"Global Well-Posedness for the Fifth-Order KdV Equation in \\\\(H^{-1}(\\\\pmb {\\\\mathbb {R}})\\\\)\",\"authors\":\"Bjoern Bringmann, Rowan Killip, Monica Visan\",\"doi\":\"10.1007/s40818-021-00111-4\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>We prove global well-posedness of the fifth-order Korteweg-de Vries equation on the real line for initial data in <span>\\\\(H^{-1}(\\\\mathbb {R})\\\\)</span>. Global well-posedness in <span>\\\\(L^2({\\\\mathbb {R}})\\\\)</span> was shown previously in [8] using the method of commuting flows. Since this method is insensitive to the ambient geometry, it cannot go beyond the sharp <span>\\\\( L^2\\\\)</span> threshold for the torus demonstrated in [3]. To prove our result, we introduce a new strategy that integrates dispersive effects into the method of commuting flows.</p></div>\",\"PeriodicalId\":36382,\"journal\":{\"name\":\"Annals of Pde\",\"volume\":\"7 2\",\"pages\":\"\"},\"PeriodicalIF\":2.4000,\"publicationDate\":\"2021-08-25\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1007/s40818-021-00111-4\",\"citationCount\":\"7\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Annals of Pde\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s40818-021-00111-4\",\"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/s40818-021-00111-4","RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
Global Well-Posedness for the Fifth-Order KdV Equation in \(H^{-1}(\pmb {\mathbb {R}})\)
We prove global well-posedness of the fifth-order Korteweg-de Vries equation on the real line for initial data in \(H^{-1}(\mathbb {R})\). Global well-posedness in \(L^2({\mathbb {R}})\) was shown previously in [8] using the method of commuting flows. Since this method is insensitive to the ambient geometry, it cannot go beyond the sharp \( L^2\) threshold for the torus demonstrated in [3]. To prove our result, we introduce a new strategy that integrates dispersive effects into the method of commuting flows.
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