Existence and stability results for 3-D regular flows of viscoelastic fluids of White--Metzner type
type: Item
instance of: scholarly article
title: Existence and stability results for 3-D regular flows of viscoelastic fluids of White--Metzner type
zbMATH Open document ID: 1081.76007
author: Raafat Talhouk
author: Luc Molinet
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2004-10-01T00:00:00Z
review text: The authors generalize results obtained by \textit{A. Hakim} [J. Math. Anal. Appl. 185, No. 3, 675--705 (1994; Zbl 0807.76002)] for incompressible viscoelastic fluids of White-Metzner type. While Hakim studied the two-dimensional case, the main theorems here are concerned with (i) local existence and uniqueness of a regular solution in three dimensions; (ii) global existence of regular solutions in three dimensions; (iii) improved global existence in two dimensions (without the smallness restriction for the retardation parameter and the boundedness hypothesis on the relaxation function). Finally, by a classical stability argument, the existence and stability of small periodic and stationary solutions are obtained.
reviewed by: M. Bildhauer
Mathematics Subject Classification ID: 76A10
Mathematics Subject Classification ID: 35Q35
zbMATH DE Number: 2105449
zbMATH Keywords: global existence
zbMATH Keywords: periodic solutions
MaRDI profile type: Publication
full work available at URL: j.na.2004.05.014
OpenAlex ID: W1987813761
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DOI: 10.1016/J.NA.2004.05.014
description: scientific article; zbMATH DE number 2105449