A 3D non-stationary Boussinesq system with Navier-slip boundary conditions. (English) Zbl 1500.35240
Summary: In this paper we study a 3D non-stationary Boussinesq system with Navier-slip boundary conditions for the velocity field and Neumann boundary conditions for the temperature. Considering the viscosity and diffusion coefficient as explicit functions depending on the temperature, we prove the existence of weak solutions and present a regularity result that allow us obtain global-in-time strong solutions.
MSC:
| 35Q35 | PDEs in connection with fluid mechanics |
| 76D03 | Existence, uniqueness, and regularity theory for incompressible viscous fluids |
| 35D30 | Weak solutions to PDEs |
| 35D35 | Strong solutions to PDEs |
| 35B65 | Smoothness and regularity of solutions to PDEs |
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