与Benjamin-Ono方程的高阶守恒定律相关的高斯测度

IF 1.3 1区数学 Q1 MATHEMATICS

Annales Scientifiques De L Ecole Normale Superieure Pub Date : 2011-09-24 DOI:10.24033/ASENS.2189

N. Tzvetkov, N. Visciglia

{"title":"与Benjamin-Ono方程的高阶守恒定律相关的高斯测度","authors":"N. Tzvetkov, N. Visciglia","doi":"10.24033/ASENS.2189","DOIUrl":null,"url":null,"abstract":"Inspired by the work of Zhidkov on the KdV equation, we perform a construction of weighted gaussian measures associated to the higher order conservation laws of the Benjamin-Ono equation. The resulting measures are supported by Sobolev spaces of increasing regularity. We also prove a property on the support of these measures leading to the conjecture that they are indeed invariant by the flow of the Benjamin-Ono equation.","PeriodicalId":50971,"journal":{"name":"Annales Scientifiques De L Ecole Normale Superieure","volume":"3 1","pages":"249-299"},"PeriodicalIF":1.3000,"publicationDate":"2011-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"35","resultStr":"{\"title\":\"Gaussian measures associated to the higher order conservation laws of the Benjamin-Ono equation\",\"authors\":\"N. Tzvetkov, N. Visciglia\",\"doi\":\"10.24033/ASENS.2189\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Inspired by the work of Zhidkov on the KdV equation, we perform a construction of weighted gaussian measures associated to the higher order conservation laws of the Benjamin-Ono equation. The resulting measures are supported by Sobolev spaces of increasing regularity. We also prove a property on the support of these measures leading to the conjecture that they are indeed invariant by the flow of the Benjamin-Ono equation.\",\"PeriodicalId\":50971,\"journal\":{\"name\":\"Annales Scientifiques De L Ecole Normale Superieure\",\"volume\":\"3 1\",\"pages\":\"249-299\"},\"PeriodicalIF\":1.3000,\"publicationDate\":\"2011-09-24\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"35\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Annales Scientifiques De L Ecole Normale Superieure\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.24033/ASENS.2189\",\"RegionNum\":1,\"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":"Annales Scientifiques De L Ecole Normale Superieure","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.24033/ASENS.2189","RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 35

摘要

受Zhidkov在KdV方程上的工作的启发，我们执行了与Benjamin-Ono方程的高阶守恒律相关的加权高斯测度的构造。所得到的测度由增加正则性的Sobolev空间支持。我们还通过Benjamin-Ono方程的流动证明了这些测度的支持的一个性质，从而得出它们确实是不变的猜想。

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

Gaussian measures associated to the higher order conservation laws of the Benjamin-Ono equation

Inspired by the work of Zhidkov on the KdV equation, we perform a construction of weighted gaussian measures associated to the higher order conservation laws of the Benjamin-Ono equation. The resulting measures are supported by Sobolev spaces of increasing regularity. We also prove a property on the support of these measures leading to the conjecture that they are indeed invariant by the flow of the Benjamin-Ono equation.

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

Annales Scientifiques De L Ecole Normale Superieure 数学-数学

CiteScore

3.00

自引率

5.30%

发文量

审稿时长

>12 weeks

期刊介绍： The Annales scientifiques de l''École normale supérieure were founded in 1864 by Louis Pasteur. The journal dealt with subjects touching on Physics, Chemistry and Natural Sciences. Around the turn of the century, it was decided that the journal should be devoted to Mathematics. Today, the Annales are open to all fields of mathematics. The Editorial Board, with the help of referees, selects articles which are mathematically very substantial. The Journal insists on maintaining a tradition of clarity and rigour in the exposition. The Annales scientifiques de l''École normale supérieures have been published by Gauthier-Villars unto 1997, then by Elsevier from 1999 to 2007. Since January 2008, they are published by the Société Mathématique de France.