具有奇异相互作用的无限多粒子非线性Hartree方程的全局适定性

IF 1.7 2区 数学 Q1 MATHEMATICS
Sonae Hadama , Younghun Hong
{"title":"具有奇异相互作用的无限多粒子非线性Hartree方程的全局适定性","authors":"Sonae Hadama ,&nbsp;Younghun Hong","doi":"10.1016/j.jfa.2025.111102","DOIUrl":null,"url":null,"abstract":"<div><div>The nonlinear Hartree equation (NLH) in the Heisenberg picture admits steady states of the form <span><math><msub><mrow><mi>γ</mi></mrow><mrow><mi>f</mi></mrow></msub><mo>=</mo><mi>f</mi><mo>(</mo><mo>−</mo><mi>Δ</mi><mo>)</mo></math></span> representing quantum states of infinitely many particles. In this article, we consider the time evolution of perturbations from a large class of such steady states via the three-dimensional NLH. We prove that if the interaction potential <em>w</em> has finite measure and initial states have finite relative entropy, then solutions preserve the relative free energy, and they exist globally in time. This result extends the important work of Lewin and Sabin <span><span>[31]</span></span> to singular interactions.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"289 9","pages":"Article 111102"},"PeriodicalIF":1.7000,"publicationDate":"2025-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Global well-posedness of the nonlinear Hartree equation for infinitely many particles with singular interaction\",\"authors\":\"Sonae Hadama ,&nbsp;Younghun Hong\",\"doi\":\"10.1016/j.jfa.2025.111102\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>The nonlinear Hartree equation (NLH) in the Heisenberg picture admits steady states of the form <span><math><msub><mrow><mi>γ</mi></mrow><mrow><mi>f</mi></mrow></msub><mo>=</mo><mi>f</mi><mo>(</mo><mo>−</mo><mi>Δ</mi><mo>)</mo></math></span> representing quantum states of infinitely many particles. In this article, we consider the time evolution of perturbations from a large class of such steady states via the three-dimensional NLH. We prove that if the interaction potential <em>w</em> has finite measure and initial states have finite relative entropy, then solutions preserve the relative free energy, and they exist globally in time. This result extends the important work of Lewin and Sabin <span><span>[31]</span></span> to singular interactions.</div></div>\",\"PeriodicalId\":15750,\"journal\":{\"name\":\"Journal of Functional Analysis\",\"volume\":\"289 9\",\"pages\":\"Article 111102\"},\"PeriodicalIF\":1.7000,\"publicationDate\":\"2025-06-18\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Functional Analysis\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0022123625002848\",\"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 Functional Analysis","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0022123625002848","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0

摘要

海森堡图中的非线性Hartree方程(NLH)承认形式为γf=f(−Δ)的稳态,表示无限多个粒子的量子态。在这篇文章中,我们通过三维NLH考虑了一大类这样的稳定状态的扰动的时间演化。证明了如果相互作用势w具有有限测度,初始态具有有限相对熵,则解保持相对自由能,且解在时间上全局存在。这一结果将Lewin和Sabin[31]的重要工作扩展到奇异相互作用。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Global well-posedness of the nonlinear Hartree equation for infinitely many particles with singular interaction
The nonlinear Hartree equation (NLH) in the Heisenberg picture admits steady states of the form γf=f(Δ) representing quantum states of infinitely many particles. In this article, we consider the time evolution of perturbations from a large class of such steady states via the three-dimensional NLH. We prove that if the interaction potential w has finite measure and initial states have finite relative entropy, then solutions preserve the relative free energy, and they exist globally in time. This result extends the important work of Lewin and Sabin [31] to singular interactions.
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
CiteScore
3.20
自引率
5.90%
发文量
271
审稿时长
7.5 months
期刊介绍: The Journal of Functional Analysis presents original research papers in all scientific disciplines in which modern functional analysis plays a basic role. Articles by scientists in a variety of interdisciplinary areas are published. Research Areas Include: • Significant applications of functional analysis, including those to other areas of mathematics • New developments in functional analysis • Contributions to important problems in and challenges to functional analysis
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
确定
请完成安全验证×
copy
已复制链接
快去分享给好友吧!
我知道了
右上角分享
点击右上角分享
0
联系我们:info@booksci.cn Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:604180095
Book学术官方微信