{"title":"Asymptotic limit of a Navier-Stokes-Korteweg system with density-dependent viscosity","authors":"Jianwei Yang, Peng Cheng, Yudong Wang","doi":"10.3934/ERA.2015.22.20","DOIUrl":null,"url":null,"abstract":"In this paper, we study a combined incompressible and vanishing \ncapillarity limit in the barotropic compressible \nNavier-Stokes-Korteweg equations for weak solutions. For well \nprepared initial data, the convergence of solutions of the \ncompressible Navier-Stokes-Korteweg equations to the \nsolutions of the incompressible Navier-Stokes equation are justified \nrigorously by adapting the modulated energy method. Furthermore, the \ncorresponding convergence rates are also obtained.","PeriodicalId":53151,"journal":{"name":"Electronic Research Announcements in Mathematical Sciences","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2015-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Electronic Research Announcements in Mathematical Sciences","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.3934/ERA.2015.22.20","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: 1
Abstract
In this paper, we study a combined incompressible and vanishing
capillarity limit in the barotropic compressible
Navier-Stokes-Korteweg equations for weak solutions. For well
prepared initial data, the convergence of solutions of the
compressible Navier-Stokes-Korteweg equations to the
solutions of the incompressible Navier-Stokes equation are justified
rigorously by adapting the modulated energy method. Furthermore, the
corresponding convergence rates are also obtained.
期刊介绍：
Electronic Research Archive (ERA), formerly known as Electronic Research Announcements in Mathematical Sciences, rapidly publishes original and expository full-length articles of significant advances in all branches of mathematics. All articles should be designed to communicate their contents to a broad mathematical audience and must meet high standards for mathematical content and clarity. After review and acceptance, articles enter production for immediate publication.
ERA is the continuation of Electronic Research Announcements of the AMS published by the American Mathematical Society, 1995—2007
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