{"title":"非线性指数型Schrödinger方程的时空解析平滑效应","authors":"G. Hoshino","doi":"10.7153/dea-2023-15-05","DOIUrl":null,"url":null,"abstract":". In this paper, we consider the global Cauchy problem for the nonlinear Schr¨odinger equations with nonlinearity of exponential type in higher space dimensions n (cid:2) 2 . In particular, we study the global existence of the solutions to the Cauchy problem with small data in the framework of intersection of Sobolev and weighted Lebesgue space: H n / 2 ∩ F H n / 2 . More precisely, we show that if data decay exponentially in H n / 2 ∩ F H n / 2 then for any time t (cid:3) = 0 , solutions are real-analytic in both space and time variables and have analytic continuation.","PeriodicalId":179999,"journal":{"name":"Differential Equations & Applications","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Space-time analytic smoothing effect for the nonlinear Schrödinger equations with nonlinearity of exponential type\",\"authors\":\"G. Hoshino\",\"doi\":\"10.7153/dea-2023-15-05\",\"DOIUrl\":null,\"url\":null,\"abstract\":\". In this paper, we consider the global Cauchy problem for the nonlinear Schr¨odinger equations with nonlinearity of exponential type in higher space dimensions n (cid:2) 2 . In particular, we study the global existence of the solutions to the Cauchy problem with small data in the framework of intersection of Sobolev and weighted Lebesgue space: H n / 2 ∩ F H n / 2 . More precisely, we show that if data decay exponentially in H n / 2 ∩ F H n / 2 then for any time t (cid:3) = 0 , solutions are real-analytic in both space and time variables and have analytic continuation.\",\"PeriodicalId\":179999,\"journal\":{\"name\":\"Differential Equations & Applications\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1900-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Differential Equations & Applications\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.7153/dea-2023-15-05\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Differential Equations & Applications","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.7153/dea-2023-15-05","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 1
摘要
. 本文研究了高维n (cid:2) 2中非线性指数型Schr¨odinger方程的全局Cauchy问题。特别地,我们研究了Sobolev与加权Lebesgue空间交点框架下具有小数据的Cauchy问题:H n / 2∩F H n / 2解的整体存在性。更准确地说,我们证明了如果数据在H n / 2∩F H n / 2中呈指数衰减,那么对于任意时间t (cid:3) = 0,解在空间和时间变量上都是实解析的,并且具有解析延拓性。
Space-time analytic smoothing effect for the nonlinear Schrödinger equations with nonlinearity of exponential type
. In this paper, we consider the global Cauchy problem for the nonlinear Schr¨odinger equations with nonlinearity of exponential type in higher space dimensions n (cid:2) 2 . In particular, we study the global existence of the solutions to the Cauchy problem with small data in the framework of intersection of Sobolev and weighted Lebesgue space: H n / 2 ∩ F H n / 2 . More precisely, we show that if data decay exponentially in H n / 2 ∩ F H n / 2 then for any time t (cid:3) = 0 , solutions are real-analytic in both space and time variables and have analytic continuation.