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