{"title":"Local Weak Solution of the Isentropic Compressible Navier–Stokes Equations with Variable Viscosity","authors":"Qin Duan, Xiangdi Huang","doi":"10.1007/s00021-024-00871-6","DOIUrl":null,"url":null,"abstract":"<div><p>In this paper, we consider the 3-D compressible isentropic Navier–Stokes equations with constant shear viscosity <span>\\(\\mu \\)</span> and the bulk one <span>\\(\\lambda =b\\rho ^\\beta \\)</span>, here <i>b</i> is a positive constant, <span>\\(\\beta \\ge 0\\)</span>. This model was first introduced and well studied by Vaigant and Kazhikhov (Sib Math J 36(6):1283–1316, 1995) in 2D domain. In this paper, under the assumption that <span>\\(\\gamma >1\\)</span>, the local existence of weak solutions with higher regularity for the 3D periodic domain is established in the presence of vacuum without any smallness on the initial data. This generalize the previous paper (Desjardins in Commun Partial Differ Equ 22(5):977–1008, 1997; Huang and Yan in J Math Phys 62(11):111504, 2021) to variable viscosity coefficients. Also this is the first result concerning the local weak solution with high regularity for the Kazhikhov model in 3D case.\n</p></div>","PeriodicalId":1,"journal":{"name":"Accounts of Chemical Research","volume":null,"pages":null},"PeriodicalIF":16.4000,"publicationDate":"2024-05-19","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/s00021-024-00871-6","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
In this paper, we consider the 3-D compressible isentropic Navier–Stokes equations with constant shear viscosity \(\mu \) and the bulk one \(\lambda =b\rho ^\beta \), here b is a positive constant, \(\beta \ge 0\). This model was first introduced and well studied by Vaigant and Kazhikhov (Sib Math J 36(6):1283–1316, 1995) in 2D domain. In this paper, under the assumption that \(\gamma >1\), the local existence of weak solutions with higher regularity for the 3D periodic domain is established in the presence of vacuum without any smallness on the initial data. This generalize the previous paper (Desjardins in Commun Partial Differ Equ 22(5):977–1008, 1997; Huang and Yan in J Math Phys 62(11):111504, 2021) to variable viscosity coefficients. Also this is the first result concerning the local weak solution with high regularity for the Kazhikhov model in 3D case.
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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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