{"title":"The Cauchy Problem for the Logarithmic Schrödinger Equation Revisited","authors":"Masayuki Hayashi, Tohru Ozawa","doi":"10.1007/s00023-024-01460-z","DOIUrl":null,"url":null,"abstract":"<p>We revisit the Cauchy problem for the logarithmic Schrödinger equation and construct strong solutions in <span>\\(H^1\\)</span>, the energy space, and the <span>\\(H^2\\)</span>-energy space. The solutions are provided in a constructive way, which does not rely on compactness arguments, that a sequence of approximate solutions forms a Cauchy sequence in a complete function space and then actual convergence is shown to be in a strong sense.</p>","PeriodicalId":463,"journal":{"name":"Annales Henri Poincaré","volume":"76 1","pages":""},"PeriodicalIF":1.4000,"publicationDate":"2024-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Annales Henri Poincaré","FirstCategoryId":"4","ListUrlMain":"https://doi.org/10.1007/s00023-024-01460-z","RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"PHYSICS, MATHEMATICAL","Score":null,"Total":0}
引用次数: 0
Abstract
We revisit the Cauchy problem for the logarithmic Schrödinger equation and construct strong solutions in \(H^1\), the energy space, and the \(H^2\)-energy space. The solutions are provided in a constructive way, which does not rely on compactness arguments, that a sequence of approximate solutions forms a Cauchy sequence in a complete function space and then actual convergence is shown to be in a strong sense.
期刊介绍：
The two journals Annales de l''Institut Henri Poincaré, physique théorique and Helvetica Physical Acta merged into a single new journal under the name Annales Henri Poincaré - A Journal of Theoretical and Mathematical Physics edited jointly by the Institut Henri Poincaré and by the Swiss Physical Society.
The goal of the journal is to serve the international scientific community in theoretical and mathematical physics by collecting and publishing original research papers meeting the highest professional standards in the field. The emphasis will be on analytical theoretical and mathematical physics in a broad sense.
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