{"title":"关于二维波导上薛定谔方程的双线性限制估计","authors":"Yangkendi Deng","doi":"10.1016/j.jde.2024.11.003","DOIUrl":null,"url":null,"abstract":"<div><div>In this article, we prove a bilinear estimate for Schrödinger equations on 2d waveguide, <span><math><mi>R</mi><mo>×</mo><mi>T</mi></math></span>. We hope it may be of use in the further study of concentration compactness for cubic NLS on <span><math><mi>R</mi><mo>×</mo><mi>T</mi></math></span>.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"416 ","pages":"Pages 1825-1836"},"PeriodicalIF":2.4000,"publicationDate":"2024-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On a bilinear restriction estimate for Schrödinger equations on 2D waveguide\",\"authors\":\"Yangkendi Deng\",\"doi\":\"10.1016/j.jde.2024.11.003\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>In this article, we prove a bilinear estimate for Schrödinger equations on 2d waveguide, <span><math><mi>R</mi><mo>×</mo><mi>T</mi></math></span>. We hope it may be of use in the further study of concentration compactness for cubic NLS on <span><math><mi>R</mi><mo>×</mo><mi>T</mi></math></span>.</div></div>\",\"PeriodicalId\":15623,\"journal\":{\"name\":\"Journal of Differential Equations\",\"volume\":\"416 \",\"pages\":\"Pages 1825-1836\"},\"PeriodicalIF\":2.4000,\"publicationDate\":\"2024-11-14\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Differential Equations\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0022039624007186\",\"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":"Journal of Differential Equations","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0022039624007186","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
On a bilinear restriction estimate for Schrödinger equations on 2D waveguide
In this article, we prove a bilinear estimate for Schrödinger equations on 2d waveguide, . We hope it may be of use in the further study of concentration compactness for cubic NLS on .
期刊介绍:
The Journal of Differential Equations is concerned with the theory and the application of differential equations. The articles published are addressed not only to mathematicians but also to those engineers, physicists, and other scientists for whom differential equations are valuable research tools.
Research Areas Include:
• Mathematical control theory
• Ordinary differential equations
• Partial differential equations
• Stochastic differential equations
• Topological dynamics
• Related topics