立方相互作用线性动力学方程中的正则效应

IF 2.4 2区数学 Q1 MATHEMATICS

Journal of Differential Equations Pub Date : 2024-09-05 DOI:10.1016/j.jde.2024.08.073

M. Escobedo

{"title":"立方相互作用线性动力学方程中的正则效应","authors":"M. Escobedo","doi":"10.1016/j.jde.2024.08.073","DOIUrl":null,"url":null,"abstract":"<div><p>We describe regularizing effects in the linearization of a kinetic equation for nonlinear waves satisfying the Schrödinger equation in terms of weak turbulence and condensate. The problem is first considered in spaces of bounded functions with weights, where existence of solutions and some first regularity properties are proved. After a suitable change of variables the equation is written in terms of a pseudo differential operator. Homogeneity of the equation and classical arguments of freezing of coefficients may then be used to prove regularizing effect in local Sobolev type spaces.</p></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":null,"pages":null},"PeriodicalIF":2.4000,"publicationDate":"2024-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S002203962400562X/pdfft?md5=17c2f0da672b5df90addbf6b59e7997d&pid=1-s2.0-S002203962400562X-main.pdf","citationCount":"0","resultStr":"{\"title\":\"Regularizing effects in a linear kinetic equation for cubic interactions\",\"authors\":\"M. Escobedo\",\"doi\":\"10.1016/j.jde.2024.08.073\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>We describe regularizing effects in the linearization of a kinetic equation for nonlinear waves satisfying the Schrödinger equation in terms of weak turbulence and condensate. The problem is first considered in spaces of bounded functions with weights, where existence of solutions and some first regularity properties are proved. After a suitable change of variables the equation is written in terms of a pseudo differential operator. Homogeneity of the equation and classical arguments of freezing of coefficients may then be used to prove regularizing effect in local Sobolev type spaces.</p></div>\",\"PeriodicalId\":15623,\"journal\":{\"name\":\"Journal of Differential Equations\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":2.4000,\"publicationDate\":\"2024-09-05\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://www.sciencedirect.com/science/article/pii/S002203962400562X/pdfft?md5=17c2f0da672b5df90addbf6b59e7997d&pid=1-s2.0-S002203962400562X-main.pdf\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Differential Equations\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S002203962400562X\",\"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/S002203962400562X","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

我们描述了满足薛定谔方程的非线性波的动力学方程在弱湍流和凝结物方面的线性化正则效应。首先在有界函数空间中考虑了这个问题，并证明了解的存在性和一些初步的正则特性。经过适当的变量变化后，方程被写成一个伪微分算子。然后，方程的同质性和系数冻结的经典论证可用于证明局部索波列夫类型空间中的正则效应。

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

Regularizing effects in a linear kinetic equation for cubic interactions

We describe regularizing effects in the linearization of a kinetic equation for nonlinear waves satisfying the Schrödinger equation in terms of weak turbulence and condensate. The problem is first considered in spaces of bounded functions with weights, where existence of solutions and some first regularity properties are proved. After a suitable change of variables the equation is written in terms of a pseudo differential operator. Homogeneity of the equation and classical arguments of freezing of coefficients may then be used to prove regularizing effect in local Sobolev type spaces.

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 Differential Equations 数学-数学

CiteScore

4.40

自引率

8.30%

发文量

543

审稿时长

9 months

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