一维可压缩非牛顿流体Cauchy问题强解的整体存在性

IF 1.2 3区数学 Q2 MATHEMATICS, APPLIED Journal of Mathematical Fluid Mechanics Pub Date : 2023-01-05 DOI:10.1007/s00021-022-00756-6

Li Fang, Aibin Zang

{"title":"一维可压缩非牛顿流体Cauchy问题强解的整体存在性","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":"{\"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}","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

摘要

为了建立幂律指数为\(r\in (1,2).\)的一维可压缩非牛顿幂律型流体Cauchy问题强解的整体存在唯一性，通过探索克服非线性项困难的迭代方法，导出了远场存在真空时的拉格朗日坐标系下的估计。在建立了一些关键估计之后，利用无穷级数理论得到了强解的整体存在性。即构造迭代时间区间，得到一个发散的时间序列。我们的结果为柯西问题提供了可压缩非牛顿流体存在性理论的新认识。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文

微信好友朋友圈 QQ好友复制链接

本刊更多论文

Global Existence of Strong Solutions to the Cauchy Problem for a One-Dimensional Compressible Non-Newtonian Fluid

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.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Journal of Mathematical Fluid Mechanics 物理-力学

CiteScore

2.00

自引率

15.40%

发文量

审稿时长

>12 weeks

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.