Incompressible Euler as a limit of complex fluid models with Navier boundary conditions
type: Item
instance of: scholarly article
title: Incompressible Euler as a limit of complex fluid models with Navier boundary conditions
zbMATH Open document ID: 1232.35122
published in: Journal of Differential Equations
publication date: 2011-12-06T00:00:00Z
review text: The authors study an incompressible second-grade fluid equation of two or three space dimensions. This a model for visco-elastic fluid, where the stress tensor is described by two parameters: the elastic response \(\alpha\) and the viscosity \(\nu\). When \(\nu= 0\), this equation is called \(\alpha\)-Euler equation, and when \(\alpha =\nu =0\), this is the Euler equation. They study the limiting process as \(\alpha ,\nu \to 0\), from a second-grade fluid equation to the Euler equation. First they discuss the boundary conditions and show that perfect-slip boundary condition of Navier is an admissible condition for an incompressible second-grade fluid equation. In this way they formulate an initial-boundary problem, and give a definition of weak solutions for this problem. They prove that if the initial data is smooth, their weak solutions strongly converge in \(L^2\) to a solution of incompressible Euler equation as \(\alpha ,\nu \to 0\). They also prove an existence theorem of global solutions for the axisymmetric flow equations without swirl.
reviewed by: Keisuke Uchikoshi
Mathematics Subject Classification ID: 35Q31
Mathematics Subject Classification ID: 76A10
Mathematics Subject Classification ID: 35D30
Mathematics Subject Classification ID: 35B07
zbMATH DE Number: 5986526
zbMATH Keywords: second-grade fluid equations
zbMATH Keywords: \(\alpha\)-Euler equation
zbMATH Keywords: Euler equation
author: Adriana Valentina Busuioc
author: Dragoş Iftimie
author: Milton C. Lopes Filho
author: Helena J. Nussenzveig Lopes
MaRDI profile type: Publication
full work available at URL: j.jde.2011.06.007
OpenAlex ID: W2068160659
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DOI: 10.1016/J.JDE.2011.06.007
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description: scientific article; zbMATH DE number 5986526