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Compressible Navier–Stokes–Fourier flows at steady-state

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Abstract

The heat conducting compressible viscous flows are governed by the Navier–Stokes–Fourier (NSF) system. In this paper, we study the NSF system accomplished by the Newton law of cooling for the heat transfer at the boundary. On one part of the boundary, we consider the Navier slip boundary condition, while in the remaining part the inlet and outlet occur. These boundary effects are the unique sink/source to the problem under study, and others effects such as the gravity and dissipation are neglected. The existence of a weak solution is proved via a new fixed point argument. With this new approach, the weak solvability is possible in Lipschitz domains, by making recourse to \(L^q\)-Neumann problems with \(q>n\). Thus, standard existence results can be applied to auxiliary problems and the claim follows by compactness techniques. Quantitative estimates are established.

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Acknowledgements

I express my sincere gratitude to the anonymous referee for many valuable comments.

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  1. Lisbon, Portugal

    Luisa Consiglieri

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  1. Luisa Consiglieri
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Correspondence to Luisa Consiglieri.

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Communicated by Claudio Gorodski.

Dedicated to my coauthor and beloved father Victor Consiglieri.

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Consiglieri, L. Compressible Navier–Stokes–Fourier flows at steady-state. São Paulo J. Math. Sci. 15, 812–838 (2021). https://doi.org/10.1007/s40863-021-00262-z

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