{"title":"The Global Solvability of the Non-conservative Viscous Compressible Two-Fluid Model with Capillarity Effects for Some Large Initial Data","authors":"Fan Zhang, Fuyi Xu, Peng Fu","doi":"10.1007/s00021-023-00797-5","DOIUrl":null,"url":null,"abstract":"<div><p>The present paper is the continuation of works (Xu and Chi in Nonlinearity 34:164–204, 2021, Xu in The maximal regularity and its application to a multi-dimensional non-conservative viscous compressible two-fluid model with capillarity effects in <span>\\(L^{p}\\)</span>-type framework. arXiv:2201.05960, 2022). Under the assumption on the some large initial data, we obtain the existence of global strong solutions to a non-conservative viscous compressible two-fluid model with capillarity effects in any dimension <span>\\(N\\ge 2\\)</span>. Our analysis mainly relies on Fourier frequency localization technology, commutator estimate and Bony’s decomposition.</p></div>","PeriodicalId":649,"journal":{"name":"Journal of Mathematical Fluid Mechanics","volume":"25 3","pages":""},"PeriodicalIF":1.3000,"publicationDate":"2023-05-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Mathematical Fluid Mechanics","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s00021-023-00797-5","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
Abstract
The present paper is the continuation of works (Xu and Chi in Nonlinearity 34:164–204, 2021, Xu in The maximal regularity and its application to a multi-dimensional non-conservative viscous compressible two-fluid model with capillarity effects in \(L^{p}\)-type framework. arXiv:2201.05960, 2022). Under the assumption on the some large initial data, we obtain the existence of global strong solutions to a non-conservative viscous compressible two-fluid model with capillarity effects in any dimension \(N\ge 2\). Our analysis mainly relies on Fourier frequency localization technology, commutator estimate and Bony’s decomposition.
期刊介绍：
The Journal of Mathematical Fluid Mechanics (JMFM)is a forum for the publication of high-quality peer-reviewed papers on the mathematical theory of fluid mechanics, with special regards to the Navier-Stokes equations. As an important part of that, the journal encourages papers dealing with mathematical aspects of computational theory, as well as with applications in science and engineering. The journal also publishes in related areas of mathematics that have a direct bearing on the mathematical theory of fluid mechanics. All papers will be characterized by originality and mathematical rigor. For a paper to be accepted, it is not enough that it contains original results. In fact, results should be highly relevant to the mathematical theory of fluid mechanics, and meet a wide readership.
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