{"title":"Stability of planar rarefaction waves under general viscosity perturbation of the isentropic Euler system","authors":"Eduard Feireisl , Antonín Novotný","doi":"10.1016/j.anihpc.2021.01.001","DOIUrl":null,"url":null,"abstract":"<div><p>We consider the vanishing viscosity limit for a model of a general non-Newtonian compressible fluid in <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>d</mi></mrow></msup></math></span>, <span><math><mi>d</mi><mo>=</mo><mn>2</mn><mo>,</mo><mn>3</mn></math></span><span>. We suppose that the initial data<span><span> approach a profile determined by the Riemann data generating a planar rarefaction wave for the isentropic Euler system. Under these circumstances the associated sequence of dissipative solutions approaches the corresponding rarefaction wave strongly in the energy norm in the vanishing viscosity limit. The result covers the particular case of a linearly </span>viscous fluid governed by the Navier–Stokes system.</span></span></p></div>","PeriodicalId":55514,"journal":{"name":"Annales De L Institut Henri Poincare-Analyse Non Lineaire","volume":"38 6","pages":"Pages 1725-1737"},"PeriodicalIF":1.8000,"publicationDate":"2021-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.anihpc.2021.01.001","citationCount":"5","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Annales De L Institut Henri Poincare-Analyse Non Lineaire","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0294144921000202","RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 5
Abstract
We consider the vanishing viscosity limit for a model of a general non-Newtonian compressible fluid in , . We suppose that the initial data approach a profile determined by the Riemann data generating a planar rarefaction wave for the isentropic Euler system. Under these circumstances the associated sequence of dissipative solutions approaches the corresponding rarefaction wave strongly in the energy norm in the vanishing viscosity limit. The result covers the particular case of a linearly viscous fluid governed by the Navier–Stokes system.
期刊介绍:
The Nonlinear Analysis section of the Annales de l''Institut Henri Poincaré is an international journal created in 1983 which publishes original and high quality research articles. It concentrates on all domains concerned with nonlinear analysis, specially applicable to PDE, mechanics, physics, economy, without overlooking the numerical aspects.