Abstract
We study a boundary value problem for a mathematical model describing the nonisothermal steady-state flow of a viscous fluid in a 3D (or 2D) bounded domain with locally Lipschitz boundary. The heat and mass transfer model considered here has the feature that a regularized Rayleigh dissipation function is used in the energy balance equation. This permits taking into account the energy dissipation due to the viscous friction effect. A theorem on the existence of a weak solution is proved under natural assumptions on the model data. Moreover, we establish extra conditions guaranteeing that the weak solution is unique and/or strong.
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Translated from Matematicheskie Zametki, 2024, Vol. 115, pp. 665–678 https://doi.org/10.4213/mzm14163.
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Baranovskii, E.S. The Stationary Navier–Stokes–Boussinesq System with a Regularized Dissipation Function. Math Notes 115, 670–682 (2024). https://doi.org/10.1134/S0001434624050031
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DOI: https://doi.org/10.1134/S0001434624050031