{"title":"Global Existence of Strong Solutions to the Cauchy Problem for a One-Dimensional Compressible Non-Newtonian Fluid","authors":"Li Fang, Aibin Zang","doi":"10.1007/s00021-022-00756-6","DOIUrl":null,"url":null,"abstract":"<div><p>This work is devoted to establish the global existence and uniqueness of strong solutions to the Cauchy problem for a one-dimensional compressible non-Newtonian fluid of power-law type, whose power-law exponent is <span>\\(r\\in (1,2).\\)</span> For this purpose, the estimates in Lagrangian coordinates is derived for the presence of vacuum at far field, by exploring the iterative method to overcome the difficulty from the nonlinear term. After establishing some key estimates, we use the theory of infinity series to obtain the global existence of strong solutions. That is, we construct the iterative time interval to obtain a divergent series of time. Our results provide a new understanding of the existence theory of compressible non-Newtonian fluids for the Cauchy problem.</p></div>","PeriodicalId":649,"journal":{"name":"Journal of Mathematical Fluid Mechanics","volume":null,"pages":null},"PeriodicalIF":1.2000,"publicationDate":"2023-01-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Mathematical Fluid Mechanics","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s00021-022-00756-6","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: 1
Abstract
This work is devoted to establish the global existence and uniqueness of strong solutions to the Cauchy problem for a one-dimensional compressible non-Newtonian fluid of power-law type, whose power-law exponent is \(r\in (1,2).\) For this purpose, the estimates in Lagrangian coordinates is derived for the presence of vacuum at far field, by exploring the iterative method to overcome the difficulty from the nonlinear term. After establishing some key estimates, we use the theory of infinity series to obtain the global existence of strong solutions. That is, we construct the iterative time interval to obtain a divergent series of time. Our results provide a new understanding of the existence theory of compressible non-Newtonian fluids for the Cauchy problem.
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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