{"title":"具有谐波势的$2d$ NLS的Sobolev范数的增长","authors":"F. Planchon, N. Tzvetkov, N. Visciglia","doi":"10.4171/rmi/1371","DOIUrl":null,"url":null,"abstract":"Abstract. We prove polynomial upper bounds on the growth of solutions to 2d cubic NLS where the Laplacian is confined by the harmonic potential. Due to better bilinear effects our bounds improve on those available for the 2d cubic NLS in the periodic setting: our growth rate for a Sobolev norm of order s = 2k, k ∈ N, is t2(s−1)/3+ε. In the appendix we provide an direct proof, based on integration by parts, of bilinear estimates associated with the harmonic oscillator.","PeriodicalId":49604,"journal":{"name":"Revista Matematica Iberoamericana","volume":" ","pages":""},"PeriodicalIF":1.3000,"publicationDate":"2021-10-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":"{\"title\":\"Growth of Sobolev norms for $2d$ NLS with harmonic potential\",\"authors\":\"F. Planchon, N. Tzvetkov, N. Visciglia\",\"doi\":\"10.4171/rmi/1371\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Abstract. We prove polynomial upper bounds on the growth of solutions to 2d cubic NLS where the Laplacian is confined by the harmonic potential. Due to better bilinear effects our bounds improve on those available for the 2d cubic NLS in the periodic setting: our growth rate for a Sobolev norm of order s = 2k, k ∈ N, is t2(s−1)/3+ε. In the appendix we provide an direct proof, based on integration by parts, of bilinear estimates associated with the harmonic oscillator.\",\"PeriodicalId\":49604,\"journal\":{\"name\":\"Revista Matematica Iberoamericana\",\"volume\":\" \",\"pages\":\"\"},\"PeriodicalIF\":1.3000,\"publicationDate\":\"2021-10-28\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"2\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Revista Matematica Iberoamericana\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.4171/rmi/1371\",\"RegionNum\":2,\"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":"Revista Matematica Iberoamericana","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.4171/rmi/1371","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
Growth of Sobolev norms for $2d$ NLS with harmonic potential
Abstract. We prove polynomial upper bounds on the growth of solutions to 2d cubic NLS where the Laplacian is confined by the harmonic potential. Due to better bilinear effects our bounds improve on those available for the 2d cubic NLS in the periodic setting: our growth rate for a Sobolev norm of order s = 2k, k ∈ N, is t2(s−1)/3+ε. In the appendix we provide an direct proof, based on integration by parts, of bilinear estimates associated with the harmonic oscillator.
期刊介绍：
Revista Matemática Iberoamericana publishes original research articles on all areas of mathematics. Its distinguished Editorial Board selects papers according to the highest standards. Founded in 1985, Revista is a scientific journal of Real Sociedad Matemática Española.
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