On the convergence of viscoelastic fluid flows to a steady state
type: Item
instance of: scholarly article
title: On the convergence of viscoelastic fluid flows to a steady state
zbMATH Open document ID: 1049.76014
author: Semuel S. P. Shen
author: Yinnian He
author: Yanping Lin
author: R. J. Tait
published in: Advances in Differential Equations
publication date: 2003-11-10T00:00:00Z
review text: This paper is concerned with the convergence of unsteady viscoelastic fluid flows to a stady state flow as time goes to infinity. The Oldroyd's mathematical model of incompressible fluids is used to describe the motion of the viscoelastic fluids, leading to generalization of the Navier-Stokes equations. By using the variational approach and various differential inequalities, the authors prove under certain assumptions that solutions to an initial boundary value problem for the unsteady viscoelatic fluid flows converge to a steady state solution exponentially and polynomially as time tends to infinity. As a consequence, the convergence to a steady state solution of the Navier-Stokes flows is a special case of this paper.
reviewed by: Song Jiang
Mathematics Subject Classification ID: 76D03
Mathematics Subject Classification ID: 76A10
Mathematics Subject Classification ID: 35B40
Mathematics Subject Classification ID: 35B35
Mathematics Subject Classification ID: 35Q35
zbMATH DE Number: 1983417
zbMATH Keywords: viscoelastic fluids
zbMATH Keywords: convergence of unsteady solutions
zbMATH Keywords: steady state solutions
zbMATH Keywords: exponential and polynomial convergence
zbMATH Keywords: variational approach
zbMATH Keywords: differential inequalities
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1983417