On the existence of solutions to generalized Navier-Stokes-Fourier system with dissipative heating

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URI: https://hdl.handle.net/10902/35419
ISSN: 1572-9648
ISSN: 0025-6455
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Autoría
Abbatiello, Anna; Bulícek, Miroslav; Lear Claveras, DanielAutoridad Unican
Fecha
2024-10
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This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made.
Publicado en
Meccanica, 2024, 59(10), 1703-1730
Editorial
Springer Netherlands
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Palabras clave
Navier–Stokes–Fourier equations
Dissipative heating
Oberbeck–Boussinesq system
Non-Newtonian fluids
Large-data existence
Resumen/Abstract
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.
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This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made.Excepto si se señala otra cosa, la licencia del ítem se describe como This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made.