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arXiv · 2401.17030

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

Anna Abbatiello·Miroslav Bulicek·Daniel Lear
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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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Anna Abbatiello, Miroslav Bulicek, Daniel Lear. 2024-01-30. On the existence of solutions to generalized Navier--Stokes--Fourier system with dissipative heating. https://arxiv.org/abs/2401.17030

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