{"title":"The regularity of the solutions to the Muskat equation: The degenerate regularity near the turnover points","authors":"Jia Shi","doi":"10.1016/j.aim.2024.109850","DOIUrl":null,"url":null,"abstract":"<div><p>In this paper, we prove that if a solution to the Muskat problem with different densities and the same viscosity is sufficiently smooth, the solution is analytic in a region that degenerates at the turnover points, provided some additional conditions are satisfied. This paper studies the analyticity of the solution near turnover points, complementing the result in <span><span>[38]</span></span>.</p></div>","PeriodicalId":50860,"journal":{"name":"Advances in Mathematics","volume":"454 ","pages":"Article 109850"},"PeriodicalIF":1.5000,"publicationDate":"2024-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Advances in Mathematics","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0001870824003657","RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"2024/8/1 0:00:00","PubModel":"Epub","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
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Abstract
In this paper, we prove that if a solution to the Muskat problem with different densities and the same viscosity is sufficiently smooth, the solution is analytic in a region that degenerates at the turnover points, provided some additional conditions are satisfied. This paper studies the analyticity of the solution near turnover points, complementing the result in [38].
期刊介绍：
Emphasizing contributions that represent significant advances in all areas of pure mathematics, Advances in Mathematics provides research mathematicians with an effective medium for communicating important recent developments in their areas of specialization to colleagues and to scientists in related disciplines.
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