{"title":"Solvability for the Ginzburg-Landau equation linearized at the degree-one vortex","authors":"Manuel del Pino, Rowan Juneman, Monica Musso","doi":"10.1016/j.jfa.2025.111105","DOIUrl":null,"url":null,"abstract":"<div><div>We consider the Ginzburg-Landau equation in the plane linearized around the standard degree-one vortex solution <span><math><mi>W</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><mi>w</mi><mo>(</mo><mi>r</mi><mo>)</mo><msup><mrow><mi>e</mi></mrow><mrow><mi>i</mi><mi>θ</mi></mrow></msup></math></span>. Using explicit representation formulae for the Fourier modes in <em>θ</em>, we obtain sharp estimates for the inverse of the linearized operator which hold for a large class of right-hand sides. This theory can be applied, for example, to estimate the inverse after dropping the usual orthogonality conditions.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"289 9","pages":"Article 111105"},"PeriodicalIF":1.7000,"publicationDate":"2025-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Functional Analysis","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0022123625002873","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
Abstract
We consider the Ginzburg-Landau equation in the plane linearized around the standard degree-one vortex solution . Using explicit representation formulae for the Fourier modes in θ, we obtain sharp estimates for the inverse of the linearized operator which hold for a large class of right-hand sides. This theory can be applied, for example, to estimate the inverse after dropping the usual orthogonality conditions.
期刊介绍:
The Journal of Functional Analysis presents original research papers in all scientific disciplines in which modern functional analysis plays a basic role. Articles by scientists in a variety of interdisciplinary areas are published.
Research Areas Include:
• Significant applications of functional analysis, including those to other areas of mathematics
• New developments in functional analysis
• Contributions to important problems in and challenges to functional analysis