Rigorous derivation of the Oberbeck-Boussinesq approximation revealing unexpected term

0577220 - MÚ 2024 RIV DE eng J - Journal Article
Bella, P. - Feireisl, Eduard - Oschmann, Florian
Rigorous derivation of the Oberbeck-Boussinesq approximation revealing unexpected term.
Communications in Mathematical Physics. Roč. 403, č. 3 (2023), s. 1245-1273. ISSN 0010-3616. E-ISSN 1432-0916
R&D Projects: GA ČR(CZ) GA21-02411S
Institutional support: RVO:67985840
Keywords : Oberbeck-Boussinesq approximation * Navier-Stokes-Fourier system * Mach number
OECD category: Pure mathematics
Impact factor: 2.4, year: 2022
Method of publishing: Open access
https://doi.org/10.1007/s00220-023-04823-5

We consider a general compressible viscous and heat conducting fluid confined between two parallel plates and heated from the bottom. The time evolution of the fluid is described by the Navier-Stokes-Fourier system considered in the regime of low Mach and Froude numbers suitably interrelated. Surprisingly and differently to the case of Neumann boundary conditions for the temperature, the asymptotic limit is identified as the Oberbeck-Boussinesq system supplemented with non-local boundary conditions for the temperature deviation.
Permanent Link: https://hdl.handle.net/11104/0346436