The Oberbeck–Boussinesq system with non-local boundary conditions

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