Rn 上分数随机延迟复合金兹堡-朗道方程的周期量的存在性

IF 1.2 3区物理与天体物理 Q3 PHYSICS, MATHEMATICAL

Journal of Mathematical Physics Pub Date : 2024-06-27 DOI:10.1063/5.0180975

Zhiyu Li, Xiaomin Song, Gang He, Ji Shu

{"title":"Rn 上分数随机延迟复合金兹堡-朗道方程的周期量的存在性","authors":"Zhiyu Li, Xiaomin Song, Gang He, Ji Shu","doi":"10.1063/5.0180975","DOIUrl":null,"url":null,"abstract":"This paper is concerned with periodic measures of fractional stochastic complex Ginzburg–Landau equations with variable time delay on unbounded domains. We first derive the uniform estimates of solutions. Then we establish the regularity and prove the equicontinuity of solutions in probability, which is used to prove the tightness of distributions of solutions. In order to overcome the non-compactness of Sobolev embeddings on unbounded domains, we use the uniform estimates on the tails in probability. As a result, we prove the existence of periodic measures by combining Arzelà-Ascoli theorem and Krylov-Bogolyubov method.","PeriodicalId":16174,"journal":{"name":"Journal of Mathematical Physics","volume":"76 1","pages":""},"PeriodicalIF":1.2000,"publicationDate":"2024-06-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Existence of periodic measures of fractional stochastic delay complex Ginzburg-Landau equations on Rn\",\"authors\":\"Zhiyu Li, Xiaomin Song, Gang He, Ji Shu\",\"doi\":\"10.1063/5.0180975\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"This paper is concerned with periodic measures of fractional stochastic complex Ginzburg–Landau equations with variable time delay on unbounded domains. We first derive the uniform estimates of solutions. Then we establish the regularity and prove the equicontinuity of solutions in probability, which is used to prove the tightness of distributions of solutions. In order to overcome the non-compactness of Sobolev embeddings on unbounded domains, we use the uniform estimates on the tails in probability. As a result, we prove the existence of periodic measures by combining Arzelà-Ascoli theorem and Krylov-Bogolyubov method.\",\"PeriodicalId\":16174,\"journal\":{\"name\":\"Journal of Mathematical Physics\",\"volume\":\"76 1\",\"pages\":\"\"},\"PeriodicalIF\":1.2000,\"publicationDate\":\"2024-06-27\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Mathematical Physics\",\"FirstCategoryId\":\"101\",\"ListUrlMain\":\"https://doi.org/10.1063/5.0180975\",\"RegionNum\":3,\"RegionCategory\":\"物理与天体物理\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"PHYSICS, MATHEMATICAL\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Mathematical Physics","FirstCategoryId":"101","ListUrlMain":"https://doi.org/10.1063/5.0180975","RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"PHYSICS, MATHEMATICAL","Score":null,"Total":0}

引用次数: 0

摘要

本文关注无界域上具有可变时延的分数随机复数金兹堡-朗道方程的周期性度量。我们首先推导了解的均匀估计。然后，我们建立了正则性，并证明了解在概率上的等连续性，进而证明了解分布的紧密性。为了克服索波列夫嵌入在无界域上的不紧凑性，我们使用了概率中对尾部的均匀估计。因此，我们结合 Arzelà-Ascoli 定理和 Krylov-Bogolyubov 方法证明了周期量的存在性。

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

Existence of periodic measures of fractional stochastic delay complex Ginzburg-Landau equations on Rn

This paper is concerned with periodic measures of fractional stochastic complex Ginzburg–Landau equations with variable time delay on unbounded domains. We first derive the uniform estimates of solutions. Then we establish the regularity and prove the equicontinuity of solutions in probability, which is used to prove the tightness of distributions of solutions. In order to overcome the non-compactness of Sobolev embeddings on unbounded domains, we use the uniform estimates on the tails in probability. As a result, we prove the existence of periodic measures by combining Arzelà-Ascoli theorem and Krylov-Bogolyubov method.

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

Journal of Mathematical Physics 物理-物理：数学物理

CiteScore

2.20

自引率

15.40%

发文量

396

审稿时长

4.3 months

期刊介绍： Since 1960, the Journal of Mathematical Physics (JMP) has published some of the best papers from outstanding mathematicians and physicists. JMP was the first journal in the field of mathematical physics and publishes research that connects the application of mathematics to problems in physics, as well as illustrates the development of mathematical methods for such applications and for the formulation of physical theories. The Journal of Mathematical Physics (JMP) features content in all areas of mathematical physics. Specifically, the articles focus on areas of research that illustrate the application of mathematics to problems in physics, the development of mathematical methods for such applications, and for the formulation of physical theories. The mathematics featured in the articles are written so that theoretical physicists can understand them. JMP also publishes review articles on mathematical subjects relevant to physics as well as special issues that combine manuscripts on a topic of current interest to the mathematical physics community. JMP welcomes original research of the highest quality in all active areas of mathematical physics, including the following: Partial Differential Equations Representation Theory and Algebraic Methods Many Body and Condensed Matter Physics Quantum Mechanics - General and Nonrelativistic Quantum Information and Computation Relativistic Quantum Mechanics, Quantum Field Theory, Quantum Gravity, and String Theory General Relativity and Gravitation Dynamical Systems Classical Mechanics and Classical Fields Fluids Statistical Physics Methods of Mathematical Physics.