{"title":"Vanishing Micro-Rotation and Angular Viscosities Limit for the 2D Micropolar Equations in a Bounded Domain","authors":"Yangyang Chu, Yuelong Xiao","doi":"10.1007/s10440-023-00596-0","DOIUrl":null,"url":null,"abstract":"<div><p>In this paper, we investigate the vanishing micro-rotation and angular viscosities limit of solutions to the 2D incompressible micropolar equations in a bounded domain with Navier-type boundary conditions satisfied by the velocity field. In a general bounded smooth domain <span>\\(\\Omega \\)</span>, we establish the uniform <span>\\(H^{2}(\\Omega )\\)</span> estimates (independent of the micro-rotation and angular viscosities) of global strong solutions and prove the rate of convergence of viscosity solutions to the inviscid solutions in <span>\\(C(0,T;H^{1}(\\Omega ))\\)</span> for any <span>\\(T>0\\)</span>.</p></div>","PeriodicalId":53132,"journal":{"name":"Acta Applicandae Mathematicae","volume":null,"pages":null},"PeriodicalIF":1.2000,"publicationDate":"2023-08-30","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/s10440-023-00596-0","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 investigate the vanishing micro-rotation and angular viscosities limit of solutions to the 2D incompressible micropolar equations in a bounded domain with Navier-type boundary conditions satisfied by the velocity field. In a general bounded smooth domain \(\Omega \), we establish the uniform \(H^{2}(\Omega )\) estimates (independent of the micro-rotation and angular viscosities) of global strong solutions and prove the rate of convergence of viscosity solutions to the inviscid solutions in \(C(0,T;H^{1}(\Omega ))\) for any \(T>0\).
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.