On the existence of solutions to generalized Navier--Stokes--Fourier system with dissipative heating
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866916110379515904 |
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| author | Abbatiello, Anna Bulicek, Miroslav Lear, Daniel |
| author_facet | Abbatiello, Anna Bulicek, Miroslav Lear, Daniel |
| contents | We consider a flow of non-Newtonian incompressible heat conducting fluids with dissipative heating. Such system can be obtained by scaling the classical Navier--Stokes--Fourier problem. As one possible singular limit may be obtained the so-called Oberbeck--Boussinesq system. However, this model is not suitable for studying the systems with high temperature gradient. These systems are described in much better way by completing the Oberbeck--Boussinesq system by an additional dissipative heating. The satisfactory existence result for such system was however not available. In this paper we show the large-data and the long-time existence of dissipative and suitable weak solution. This is the starting point for further analysis of the stability properties of such problems. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2401_17030 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the existence of solutions to generalized Navier--Stokes--Fourier system with dissipative heating Abbatiello, Anna Bulicek, Miroslav Lear, Daniel Analysis of PDEs We consider a flow of non-Newtonian incompressible heat conducting fluids with dissipative heating. Such system can be obtained by scaling the classical Navier--Stokes--Fourier problem. As one possible singular limit may be obtained the so-called Oberbeck--Boussinesq system. However, this model is not suitable for studying the systems with high temperature gradient. These systems are described in much better way by completing the Oberbeck--Boussinesq system by an additional dissipative heating. The satisfactory existence result for such system was however not available. In this paper we show the large-data and the long-time existence of dissipative and suitable weak solution. This is the starting point for further analysis of the stability properties of such problems. |
| title | On the existence of solutions to generalized Navier--Stokes--Fourier system with dissipative heating |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2401.17030 |