The oberbeck-boussinesq approximation and rayleigh-benard convection revisited

We consider the Oberbeck-Boussinesq approximation driven by an inhomogeneous temperature distribution on the boundary of a bounded fluid domain. The relevant boundary conditions are perturbed by a non-local term arising in the incompressible limit of the Navier-Stokes-Fourier system. The long time behaviour of the resulting initial/boundary value problem is investigated.