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Existence of global weak solutions to 3D incompressible heat‐conducting motions with large flux
Author(s) -
Zadrzyńska Ewa,
Zaja̧czkowski Wojciech M.
Publication year - 2021
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.7156
Subject(s) - inflow , mathematics , neumann boundary condition , outflow , boundary value problem , compressibility , mathematical analysis , cylinder , no slip condition , slip (aerodynamics) , heat flux , dirichlet boundary condition , domain (mathematical analysis) , robin boundary condition , mixed boundary condition , mechanics , geometry , physics , heat transfer , thermodynamics , meteorology
Global existence of weak solutions to the Navier–Stokes equations coupled with the heat equation by the external force dependent on temperature is proved. The problem is considered in a cylindrical domain under boundary slip conditions and with inflow and outflow. Moreover, the Neumann boundary condition for the temperature is assumed on the lateral surface of the cylinder, while on the remaining part of the boundary, the Dirichlet condition is supposed. We derive such an estimate that inflow and outflow need not vanish as t → ∞ .