{"title":"Mathematical Analysis of a Diffuse Interface Model for Multi-phase Flows of Incompressible Viscous Fluids with Different Densities","authors":"Helmut Abels, Harald Garcke, Andrea Poiatti","doi":"10.1007/s00021-024-00864-5","DOIUrl":null,"url":null,"abstract":"<div><p>We analyze a diffuse interface model for multi-phase flows of <i>N</i> incompressible, viscous Newtonian fluids with different densities. In the case of a bounded and sufficiently smooth domain existence of weak solutions in two and three space dimensions and a singular free energy density is shown. Moreover, in two space dimensions global existence for sufficiently regular initial data is proven. In three space dimension, existence of strong solutions locally in time is shown as well as regularization for large times in the absence of exterior forces. Moreover, in both two and three dimensions, convergence to stationary solutions as time tends to infinity is proved.</p></div>","PeriodicalId":1,"journal":{"name":"Accounts of Chemical Research","volume":null,"pages":null},"PeriodicalIF":16.4000,"publicationDate":"2024-03-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Accounts of Chemical Research","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s00021-024-00864-5","RegionNum":1,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"CHEMISTRY, MULTIDISCIPLINARY","Score":null,"Total":0}
引用次数: 0
Abstract
We analyze a diffuse interface model for multi-phase flows of N incompressible, viscous Newtonian fluids with different densities. In the case of a bounded and sufficiently smooth domain existence of weak solutions in two and three space dimensions and a singular free energy density is shown. Moreover, in two space dimensions global existence for sufficiently regular initial data is proven. In three space dimension, existence of strong solutions locally in time is shown as well as regularization for large times in the absence of exterior forces. Moreover, in both two and three dimensions, convergence to stationary solutions as time tends to infinity is proved.
我们分析了 N 种不同密度的不可压缩粘性牛顿流体多相流的扩散界面模型。在有界且足够光滑的域中，证明了弱解在二维和三维空间的存在性以及奇异的自由能密度。此外，在二维空间中，对于足够规则的初始数据，证明了全局存在性。在三维空间中，证明了强解在时间上的局部存在，以及在没有外部力的情况下大时间的正则化。此外，在二维和三维空间中，当时间趋于无穷大时，都证明了向静止解的收敛性。
期刊介绍：
Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance.
Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.
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