{"title":"质量等于孤立子质量的聚焦非线性系统爆破解的确定","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":"{\"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}","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}
A Determination of the Blowup Solutions to the Focusing NLS with Mass Equal to the Mass of the Soliton
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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