{"title":"A New Blowup Criterion to the Cauchy Problem for the Three-Dimensional Compressible Viscous Micropolar Fluids with Vacuum","authors":"Xiaofeng Hou, Yinjie Xu","doi":"10.1007/s10440-024-00642-5","DOIUrl":null,"url":null,"abstract":"<div><p>In this paper, we prove a new blowup criterion for the strong solution to the Cauchy problem of three-dimensional micropolar fluid equation with vacuum. Specifically, we establish a blowup criterion in terms of <span>\\(L_{t}^{\\infty }L_{x}^{q}\\)</span> of the density, where <span>\\(1< q<\\infty \\)</span>, and it is independent on the velocity of rotation of the microscopic particles.</p></div>","PeriodicalId":53132,"journal":{"name":"Acta Applicandae Mathematicae","volume":"190 1","pages":""},"PeriodicalIF":1.2000,"publicationDate":"2024-04-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Acta Applicandae Mathematicae","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s10440-024-00642-5","RegionNum":4,"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
In this paper, we prove a new blowup criterion for the strong solution to the Cauchy problem of three-dimensional micropolar fluid equation with vacuum. Specifically, we establish a blowup criterion in terms of \(L_{t}^{\infty }L_{x}^{q}\) of the density, where \(1< q<\infty \), and it is independent on the velocity of rotation of the microscopic particles.
期刊介绍：
Acta Applicandae Mathematicae is devoted to the art and techniques of applying mathematics and the development of new, applicable mathematical methods.
Covering a large spectrum from modeling to qualitative analysis and computational methods, Acta Applicandae Mathematicae contains papers on different aspects of the relationship between theory and applications, ranging from descriptive papers on actual applications meeting contemporary mathematical standards to proofs of new and deep theorems in applied mathematics.
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