On three-dimensional flows of viscoelastic fluids of Giesekus type

Viscoelastic rate-type fluids are popular models of choice in many applications involving flows of fluid-like materials with complex micro-structure. A well-developed mathematical theory for the most of these classical fluid models is however missing. The main purpose of this study is to provide a c...

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Bibliographic Details
Published inNonlinearity Vol. 38; no. 1; pp. 15004 - 15045
Main Authors Bulíček, Miroslav, Los, Tomáš, Málek, Josef
Format Journal Article
LanguageEnglish
Published IOP Publishing 31.01.2025
Subjects
35K55
35M13
35Q35
76A10
biting limit
Burgers model
Giesekus model
large-data existence
long-time existence
viscoelasticity
weak solution
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Summary:Viscoelastic rate-type fluids are popular models of choice in many applications involving flows of fluid-like materials with complex micro-structure. A well-developed mathematical theory for the most of these classical fluid models is however missing. The main purpose of this study is to provide a complete proof of long-time and large-data existence of weak solutions to unsteady internal three-dimensional flows of Giesekus fluids subject to a no-slip boundary condition. As a new auxiliary tool, we provide the identification of certain biting limits in the parabolic setting, presented here within the framework of evolutionary Stokes problems. We also generalize the long-time and large-data existence result to higher dimensions, to viscoelastic models with multiple relaxation mechanisms and to viscoelastic models with different type of dissipation.
Bibliography:NON-107932.R1
ISSN:0951-7715
1361-6544
DOI:10.1088/1361-6544/ad7cb5