带有乘法空间白噪声的二维非线性薛定谔方程在全空间上的全局好求解性

IF 1.5 1区数学 Q2 STATISTICS & PROBABILITY Probability Theory and Related Fields Pub Date : 2024-06-22 DOI:10.1007/s00440-024-01288-y

Arnaud Debussche, Ruoyuan Liu, Nikolay Tzvetkov, Nicola Visciglia

{"title":"带有乘法空间白噪声的二维非线性薛定谔方程在全空间上的全局好求解性","authors":"Arnaud Debussche, Ruoyuan Liu, Nikolay Tzvetkov, Nicola Visciglia","doi":"10.1007/s00440-024-01288-y","DOIUrl":null,"url":null,"abstract":"<p>We consider the nonlinear Schrödinger equation with multiplicative spatial white noise and an arbitrary polynomial nonlinearity on the two-dimensional full space domain. We prove global well-posedness by using a gauge-transform introduced by Hairer and Labbé (Electron Commun Probab 20(43):11, 2015) and constructing the solution as a limit of solutions to a family of approximating equations. This paper extends a previous result by Debussche and Martin (Nonlinearity 32(4):1147–1174, 2019) with a sub-quadratic nonlinearity.\n</p>","PeriodicalId":20527,"journal":{"name":"Probability Theory and Related Fields","volume":null,"pages":null},"PeriodicalIF":1.5000,"publicationDate":"2024-06-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Global well-posedness of the 2D nonlinear Schrödinger equation with multiplicative spatial white noise on the full space\",\"authors\":\"Arnaud Debussche, Ruoyuan Liu, Nikolay Tzvetkov, Nicola Visciglia\",\"doi\":\"10.1007/s00440-024-01288-y\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>We consider the nonlinear Schrödinger equation with multiplicative spatial white noise and an arbitrary polynomial nonlinearity on the two-dimensional full space domain. We prove global well-posedness by using a gauge-transform introduced by Hairer and Labbé (Electron Commun Probab 20(43):11, 2015) and constructing the solution as a limit of solutions to a family of approximating equations. This paper extends a previous result by Debussche and Martin (Nonlinearity 32(4):1147–1174, 2019) with a sub-quadratic nonlinearity.\\n</p>\",\"PeriodicalId\":20527,\"journal\":{\"name\":\"Probability Theory and Related Fields\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.5000,\"publicationDate\":\"2024-06-22\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Probability Theory and Related Fields\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1007/s00440-024-01288-y\",\"RegionNum\":1,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"STATISTICS & PROBABILITY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Probability Theory and Related Fields","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s00440-024-01288-y","RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"STATISTICS & PROBABILITY","Score":null,"Total":0}

引用次数: 0

摘要

我们考虑了二维全空间域上具有乘法空间白噪声和任意多项式非线性的非线性薛定谔方程。我们利用 Hairer 和 Labbé（Electron Commun Probab 20(43):11, 2015）引入的规整变换，并将解构建为近似方程组的解的极限，从而证明了全局好求解性。本文扩展了 Debussche 和 Martin（《非线性》32(4):1147-1174, 2019）之前的一个结果，其中包含一个亚二次非线性。

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

微信好友朋友圈 QQ好友复制链接

本刊更多论文

Global well-posedness of the 2D nonlinear Schrödinger equation with multiplicative spatial white noise on the full space

We consider the nonlinear Schrödinger equation with multiplicative spatial white noise and an arbitrary polynomial nonlinearity on the two-dimensional full space domain. We prove global well-posedness by using a gauge-transform introduced by Hairer and Labbé (Electron Commun Probab 20(43):11, 2015) and constructing the solution as a limit of solutions to a family of approximating equations. This paper extends a previous result by Debussche and Martin (Nonlinearity 32(4):1147–1174, 2019) with a sub-quadratic nonlinearity.

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

Probability Theory and Related Fields 数学-统计学与概率论

CiteScore

3.70

自引率

5.00%

发文量

审稿时长

6-12 weeks

期刊介绍： Probability Theory and Related Fields publishes research papers in modern probability theory and its various fields of application. Thus, subjects of interest include: mathematical statistical physics, mathematical statistics, mathematical biology, theoretical computer science, and applications of probability theory to other areas of mathematics such as combinatorics, analysis, ergodic theory and geometry. Survey papers on emerging areas of importance may be considered for publication. The main languages of publication are English, French and German.