{"title":"A Determination of the Blowup Solutions to the Focusing NLS with Mass Equal to the Mass of the Soliton","authors":"Benjamin Dodson","doi":"10.1007/s40818-022-00142-5","DOIUrl":null,"url":null,"abstract":"<div><p>In this paper we prove rigidity for blowup solutions to the focusing, mass-critical nonlinear Schrödinger equation in dimensions <span>\\(2 \\le d \\le 15\\)</span> with mass equal to the mass of the soliton. We prove that the only such solutions are the solitons and the pseudoconformal transformation of the solitons. We show that this implies a Liouville result for the nonlinear Schrödinger equation.\n</p></div>","PeriodicalId":36382,"journal":{"name":"Annals of Pde","volume":"9 1","pages":""},"PeriodicalIF":2.4000,"publicationDate":"2022-12-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s40818-022-00142-5.pdf","citationCount":"7","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Annals of Pde","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s40818-022-00142-5","RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 7
Abstract
In this paper we prove rigidity for blowup solutions to the focusing, mass-critical nonlinear Schrödinger equation in dimensions \(2 \le d \le 15\) with mass equal to the mass of the soliton. We prove that the only such solutions are the solitons and the pseudoconformal transformation of the solitons. We show that this implies a Liouville result for the nonlinear Schrödinger equation.
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