On various models describing behaviour of thermoviscoelastic rate-type fluids
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866916713973415936 |
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| author | Bulìček, Miroslav Woźnicki, Jakub |
| author_facet | Bulìček, Miroslav Woźnicki, Jakub |
| contents | Viscoelastic rate-type fluid models are essential for describing the behavior of a wide range of complex materials, with applications in fields such as engineering, biomaterials, and medicine. These models are particularly useful for understanding the rheological properties of materials that exhibit both elastic and viscous behavior under deformation. However, many real-world applications involve significant thermal effects, where heat conduction and the temperature dependence of material properties must also be considered. In this paper, we introduce a thermodynamically consistent model for heat-conducting viscoelastic rate-type fluids and establish the existence of a global weak solution in a two-dimensional setting. The result holds under the condition that the initial energy and entropy are controlled in appropriate natural norms. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_03735 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On various models describing behaviour of thermoviscoelastic rate-type fluids Bulìček, Miroslav Woźnicki, Jakub Analysis of PDEs 35A01, 35Q35, 76A10, 76D03 Viscoelastic rate-type fluid models are essential for describing the behavior of a wide range of complex materials, with applications in fields such as engineering, biomaterials, and medicine. These models are particularly useful for understanding the rheological properties of materials that exhibit both elastic and viscous behavior under deformation. However, many real-world applications involve significant thermal effects, where heat conduction and the temperature dependence of material properties must also be considered. In this paper, we introduce a thermodynamically consistent model for heat-conducting viscoelastic rate-type fluids and establish the existence of a global weak solution in a two-dimensional setting. The result holds under the condition that the initial energy and entropy are controlled in appropriate natural norms. |
| title | On various models describing behaviour of thermoviscoelastic rate-type fluids |
| topic | Analysis of PDEs 35A01, 35Q35, 76A10, 76D03 |
| url | https://arxiv.org/abs/2502.03735 |