On the incompressible limit for the Navier-Stokes-Fourier system in domains with wavy bottoms

In this paper, the Oberbeck - Boussinesq approximation is identified as a singular limit of the full Navier - Stokes - Fourier system provided the Mach and Froude numbers tend to zero. The result holds for any ill-prepared initial data and without any restrictions imposed on the length of the time interval. In particular, it is shown that the velocity converges almost everywhere, the oscillations of the sound waves being effectively damped by the presence of a "wavy bottom" of the physical domain.