Abstract
We investigate the steady compressible Navier–Stokes–Fourier system in a two- or three-dimensional bounded domain, supplied with slip boundary conditions for the velocity and Dirichlet condition for the temperature. We are interested in the existence of weak solutions. In order to extend the admissible range of parameters, we also consider a slightly weaker notion of variational entropy solutions, where the total energy balance is replaced by entropy inequality. The formulation is further based on ballistic energy inequality which allows to obtain suitable a priori estimates.
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Acknowledgements
The work of T.P. was partially supported by National Science Centre grant No. 2018/29/B/ST1/00339 (Opus). The work of M.P. was partially supported by the Czech Science Foundation (GAČR), project No. 22-01591S.
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Piasecki, T., Pokorný, M. (2023). Steady Compressible Navier–Stokes–Fourier System with Slip Boundary Condition for the Velocity and Dirichlet Boundary Condition for the Temperature. In: Bodnár, T., Galdi, G.P., Nečasová, Š. (eds) Fluids Under Control. Advances in Mathematical Fluid Mechanics(). Birkhäuser, Cham. https://doi.org/10.1007/978-3-031-27625-5_8
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