{"title":"$H^1(\\mathbb{R})+H^s(\\mathbb{T})$中NLS的全局适定性","authors":"Friedrich Klaus, P. Kunstmann","doi":"10.5445/IR/1000137946","DOIUrl":null,"url":null,"abstract":"We show global wellposedness for the defocusing cubic nonlinear Schrodinger equation (NLS) in $H^1(\\mathbb{R}) + H^{3/2+}(\\mathbb{T})$, and for the defocusing NLS with polynomial nonlinearities in $H^1(\\mathbb{R}) + H^{5/2+}(\\mathbb{T})$. This complements local results for the cubic NLS [6] and global results for the quadratic NLS \n[8] in this hybrid setting.","PeriodicalId":8445,"journal":{"name":"arXiv: Analysis of PDEs","volume":"12 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2021-09-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Global wellposedness of NLS in $H^1(\\\\mathbb{R})+H^s(\\\\mathbb{T})$\",\"authors\":\"Friedrich Klaus, P. Kunstmann\",\"doi\":\"10.5445/IR/1000137946\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We show global wellposedness for the defocusing cubic nonlinear Schrodinger equation (NLS) in $H^1(\\\\mathbb{R}) + H^{3/2+}(\\\\mathbb{T})$, and for the defocusing NLS with polynomial nonlinearities in $H^1(\\\\mathbb{R}) + H^{5/2+}(\\\\mathbb{T})$. This complements local results for the cubic NLS [6] and global results for the quadratic NLS \\n[8] in this hybrid setting.\",\"PeriodicalId\":8445,\"journal\":{\"name\":\"arXiv: Analysis of PDEs\",\"volume\":\"12 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2021-09-23\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv: Analysis of PDEs\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.5445/IR/1000137946\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv: Analysis of PDEs","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.5445/IR/1000137946","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Global wellposedness of NLS in $H^1(\mathbb{R})+H^s(\mathbb{T})$
We show global wellposedness for the defocusing cubic nonlinear Schrodinger equation (NLS) in $H^1(\mathbb{R}) + H^{3/2+}(\mathbb{T})$, and for the defocusing NLS with polynomial nonlinearities in $H^1(\mathbb{R}) + H^{5/2+}(\mathbb{T})$. This complements local results for the cubic NLS [6] and global results for the quadratic NLS
[8] in this hybrid setting.
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