{"title":"小速度下$\\mathbb{R}^2中Gross-Pitaevskii方程中行波的矫顽力","authors":"D. Chiron, Eliot Pacherie","doi":"10.5565/PUBLMAT6712307","DOIUrl":null,"url":null,"abstract":"In a previous paper, we constructed a smooth branch of travelling waves for the 2 dimensional Gross-Pitaevskii equation. Here, we continue the study of this branch. We show some coercivity results, and we deduce from them the kernel of the linearized operator, a spectral stability result, as well as a uniqueness result in the energy space.","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2019-11-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"6","resultStr":"{\"title\":\"Coercivity for travelling waves in the Gross-Pitaevskii equation in $\\\\mathbb{R}^2$ for small speed\",\"authors\":\"D. Chiron, Eliot Pacherie\",\"doi\":\"10.5565/PUBLMAT6712307\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In a previous paper, we constructed a smooth branch of travelling waves for the 2 dimensional Gross-Pitaevskii equation. Here, we continue the study of this branch. We show some coercivity results, and we deduce from them the kernel of the linearized operator, a spectral stability result, as well as a uniqueness result in the energy space.\",\"PeriodicalId\":0,\"journal\":{\"name\":\"\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0,\"publicationDate\":\"2019-11-10\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"6\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.5565/PUBLMAT6712307\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.5565/PUBLMAT6712307","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Coercivity for travelling waves in the Gross-Pitaevskii equation in $\mathbb{R}^2$ for small speed
In a previous paper, we constructed a smooth branch of travelling waves for the 2 dimensional Gross-Pitaevskii equation. Here, we continue the study of this branch. We show some coercivity results, and we deduce from them the kernel of the linearized operator, a spectral stability result, as well as a uniqueness result in the energy space.