具有弱分散性的分数非线性薛定谔方程的 Gibbs 动力学

IF 2.2 1区物理与天体物理 Q1 PHYSICS, MATHEMATICAL

Communications in Mathematical Physics Pub Date : 2024-10-07 DOI:10.1007/s00220-024-05116-1

Rui Liang, Yuzhao Wang

{"title":"具有弱分散性的分数非线性薛定谔方程的 Gibbs 动力学","authors":"Rui Liang, Yuzhao Wang","doi":"10.1007/s00220-024-05116-1","DOIUrl":null,"url":null,"abstract":"<div><p>We consider the Cauchy problem for the one-dimensional periodic cubic nonlinear fractional Schrödinger equation (FNLS) with initial data distributed via its associated Gibbs measure. We construct global strong solutions with the flow property for the FNLS on the support of the Gibbs measure in the full dispersive range, thus resolving a question proposed by Sun and Tzvetkov (Nonlinear Anal 213, paper no. 112530, 2021). As a byproduct, we prove the invariance of the Gibbs measure and almost sure global well-posedness for FNLS.\n</p></div>","PeriodicalId":522,"journal":{"name":"Communications in Mathematical Physics","volume":"405 10","pages":""},"PeriodicalIF":2.2000,"publicationDate":"2024-10-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00220-024-05116-1.pdf","citationCount":"0","resultStr":"{\"title\":\"Gibbs Dynamics for Fractional Nonlinear Schrödinger Equations with Weak Dispersion\",\"authors\":\"Rui Liang, Yuzhao Wang\",\"doi\":\"10.1007/s00220-024-05116-1\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>We consider the Cauchy problem for the one-dimensional periodic cubic nonlinear fractional Schrödinger equation (FNLS) with initial data distributed via its associated Gibbs measure. We construct global strong solutions with the flow property for the FNLS on the support of the Gibbs measure in the full dispersive range, thus resolving a question proposed by Sun and Tzvetkov (Nonlinear Anal 213, paper no. 112530, 2021). As a byproduct, we prove the invariance of the Gibbs measure and almost sure global well-posedness for FNLS.\\n</p></div>\",\"PeriodicalId\":522,\"journal\":{\"name\":\"Communications in Mathematical Physics\",\"volume\":\"405 10\",\"pages\":\"\"},\"PeriodicalIF\":2.2000,\"publicationDate\":\"2024-10-07\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://link.springer.com/content/pdf/10.1007/s00220-024-05116-1.pdf\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Communications in Mathematical Physics\",\"FirstCategoryId\":\"101\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s00220-024-05116-1\",\"RegionNum\":1,\"RegionCategory\":\"物理与天体物理\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"PHYSICS, MATHEMATICAL\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Communications in Mathematical Physics","FirstCategoryId":"101","ListUrlMain":"https://link.springer.com/article/10.1007/s00220-024-05116-1","RegionNum":1,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"PHYSICS, MATHEMATICAL","Score":null,"Total":0}

引用次数: 0

摘要

我们考虑了一维周期性立方非线性分数薛定谔方程（FNLS）的考奇问题，其初始数据通过相关的吉布斯量分布。我们为 FNLS 在全分散范围内的 Gibbs 量支持上构建了具有流动特性的全局强解，从而解决了 Sun 和 Tzvetkov 提出的一个问题（《非线性分析》213 期，论文编号 112530，2021 年）。作为副产品，我们证明了 Gibbs 量的不变性和 FNLS 几乎确定的全局可好求性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Gibbs Dynamics for Fractional Nonlinear Schrödinger Equations with Weak Dispersion

We consider the Cauchy problem for the one-dimensional periodic cubic nonlinear fractional Schrödinger equation (FNLS) with initial data distributed via its associated Gibbs measure. We construct global strong solutions with the flow property for the FNLS on the support of the Gibbs measure in the full dispersive range, thus resolving a question proposed by Sun and Tzvetkov (Nonlinear Anal 213, paper no. 112530, 2021). As a byproduct, we prove the invariance of the Gibbs measure and almost sure global well-posedness for FNLS.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Communications in Mathematical Physics 物理-物理：数学物理

CiteScore

4.70

自引率

8.30%

发文量

226

审稿时长

3-6 weeks

期刊介绍： The mission of Communications in Mathematical Physics is to offer a high forum for works which are motivated by the vision and the challenges of modern physics and which at the same time meet the highest mathematical standards.