{"title":"Exact Formulas for Esimating the Area of Flow Regions in Free Boundary Problems","authors":"M. M. Alimov","doi":"10.3103/s1066369x24700361","DOIUrl":null,"url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>An effective technique is proposed for obtaining exact formulas for estimating the area of flow regions in two-dimensional fluid flow problems with free boundaries, that allow an exact solution in terms of elliptic functions. The effectiveness of the technique is demonstrated using a specific example of the problem of capillary waves on the surface of a liquid of finite depth. This example is characterized by mirror symmetry of the flow region, but the technique can be generalized to the case of other symmetry of the flow region.</p>","PeriodicalId":46110,"journal":{"name":"Russian Mathematics","volume":"16 1","pages":""},"PeriodicalIF":0.5000,"publicationDate":"2024-08-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Russian Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.3103/s1066369x24700361","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
An effective technique is proposed for obtaining exact formulas for estimating the area of flow regions in two-dimensional fluid flow problems with free boundaries, that allow an exact solution in terms of elliptic functions. The effectiveness of the technique is demonstrated using a specific example of the problem of capillary waves on the surface of a liquid of finite depth. This example is characterized by mirror symmetry of the flow region, but the technique can be generalized to the case of other symmetry of the flow region.
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