Rigorous derivation of the Oberbeck-Boussinesq approximation revealing unexpected term. (English) Zbl 1533.35260
In this paper, the authors consider compressible viscous and heat conduction of fluids in a certain physical model. The governing equations of such a physical phenomena are obtained under reasonable conditions. Such a work seems to be the first one addressing singular limits subject to inhomogeneous Dirichlet boundary conditions imposed on the temperature. Asymptoticly, the obtained limit can be identified as the Oberbeck-Boussinesq system.
Reviewer: Igor Leite Freire (São Carlos)
MSC:
| 35Q35 | PDEs in connection with fluid mechanics |
| 76N10 | Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics |
| 76R10 | Free convection |
| 80A19 | Diffusive and convective heat and mass transfer, heat flow |
| 35B40 | Asymptotic behavior of solutions to PDEs |
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