{"title":"Well-posedness for Maxwell equations with Kerr nonlinearity in three dimensions via Strichartz estimates","authors":"R. Schippa","doi":"10.5445/IR/1000136611","DOIUrl":null,"url":null,"abstract":"We show new local well-posedness results for quasilinear Maxwell equations in three spatial dimensions with an emphasis on the Kerr nonlinearity. For this purpose, new Strichartz estimates are proved for solutions with rough permittivity by conjugation to half-wave equations. We use the Strichartz estimates in a known combination with energy estimates to derive the new well-posedness results.","PeriodicalId":8445,"journal":{"name":"arXiv: Analysis of PDEs","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2021-08-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv: Analysis of PDEs","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.5445/IR/1000136611","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 1
Abstract
We show new local well-posedness results for quasilinear Maxwell equations in three spatial dimensions with an emphasis on the Kerr nonlinearity. For this purpose, new Strichartz estimates are proved for solutions with rough permittivity by conjugation to half-wave equations. We use the Strichartz estimates in a known combination with energy estimates to derive the new well-posedness results.
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