Stability with respect to domain of the low Mach number limit of compressible heat-conducting viscous fluid

We investigate the asymptotic limit of solutions to the Navier-Stokes-Fourier system with the Mach number proportional to a small parameter $\epsilon \to 0$, the Froude number proportional to $\sqrt{\epsilon }$ and when the fluid occupies large domain with spatial obstacle of rough surface varying when $\epsilon \to 0$. The limit velocity field is solenoidal and satisfies the incompressible Oberbeck-Boussinesq approximation. Our studies are based on weak solutions approach and in order to pass to the limit in a convective term we apply the spectral analysis of the associated wave propagator (Neumann Laplacian) governing the motion of acoustic waves.