Weak sequential stability of solutions to a nonisothermal kinetic model for incompressible dilute polymeric fluids
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866918436118986752 |
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| author | Bulíček, Miroslav Málek, Josef Süli, Endre |
| author_facet | Bulíček, Miroslav Málek, Josef Süli, Endre |
| contents | The paper is concerned with the mathematical analysis of a class of thermodynamically consistent kinetic models for nonisothermal flows of dilute polymeric fluids, based on the identification of energy storage mechanisms and entropy production mechanisms in the fluid under consideration. The model involves a system of nonlinear partial differential equations coupling the unsteady incompressible temperature-dependent Navier--Stokes equations to a temperature-dependent generalization of the classical Fokker--Planck equation and an evolution equation for the absolute temperature. Sequences of smooth solutions to the initial-boundary-value problem, satisfying the available bounds that are uniform with respect to the given data of the model, are shown to converge to a global-in-time large-data weak solution that satisfies an energy inequality, where the absolute temperature satisfies a renormalized variational inequality, implying weak sequential stability of the mathematical model. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_20580 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Weak sequential stability of solutions to a nonisothermal kinetic model for incompressible dilute polymeric fluids Bulíček, Miroslav Málek, Josef Süli, Endre Analysis of PDEs 35D05, 35Q35, 46E30, 76D03, 76Z99 The paper is concerned with the mathematical analysis of a class of thermodynamically consistent kinetic models for nonisothermal flows of dilute polymeric fluids, based on the identification of energy storage mechanisms and entropy production mechanisms in the fluid under consideration. The model involves a system of nonlinear partial differential equations coupling the unsteady incompressible temperature-dependent Navier--Stokes equations to a temperature-dependent generalization of the classical Fokker--Planck equation and an evolution equation for the absolute temperature. Sequences of smooth solutions to the initial-boundary-value problem, satisfying the available bounds that are uniform with respect to the given data of the model, are shown to converge to a global-in-time large-data weak solution that satisfies an energy inequality, where the absolute temperature satisfies a renormalized variational inequality, implying weak sequential stability of the mathematical model. |
| title | Weak sequential stability of solutions to a nonisothermal kinetic model for incompressible dilute polymeric fluids |
| topic | Analysis of PDEs 35D05, 35Q35, 46E30, 76D03, 76Z99 |
| url | https://arxiv.org/abs/2510.20580 |