On three dimensional flows of viscoelastic fluids of Giesekus type
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866910383037480960 |
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| author | Bulíček, Miroslav Los, Tomáš Málek, Josef |
| author_facet | Bulíček, Miroslav Los, Tomáš Málek, Josef |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_17348 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On three dimensional flows of viscoelastic fluids of Giesekus type Bulíček, Miroslav Los, Tomáš Málek, Josef Analysis of PDEs 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. |
| title | On three dimensional flows of viscoelastic fluids of Giesekus type |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2403.17348 |