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arXiv · 2403.17348

On three dimensional flows of viscoelastic fluids of Giesekus type

Miroslav Bulíček·Tomáš Los·Josef Málek
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Abstract

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.

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Miroslav Bulíček, Tomáš Los, Josef Málek. 2024-03-26. On three dimensional flows of viscoelastic fluids of Giesekus type. https://arxiv.org/abs/2403.17348

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