The Oberbeck–Boussinesq system with non-local boundary conditions

Abstract

We consider the Oberbeck–Boussinesq system with non-local boundary conditions arising as a singular limit of the full Navier–Stokes–Fourier system in the regime of low Mach and low Froude numbers. The existence of strong solutions is shown on a maximal time interval [ 0 , T m a x ) [0, T_{\mathrm {max}}) . Moreover, T m a x = ∞ T_{\mathrm {max}} = \infty in the two-dimensional setting.