Abstract
We consider unsteady flows of compressible Navier-Stokes-Fourier equations in domains with bottoms that are not flat and where the fluid fulfils Navier's slip boundary conditions. Dealing with weak solutions whose long-time and large data existence has been recently established, we investigate their behavior for vanishing Mach number (the square of this small parameter appears also in the Navier slip condition), and prove their convergence towards the weak solution of the so-called Boussinesq approximation with the no-slip boundary condition. The fact that we treat the Navier boundary condition brings several interesting features in the analysis of acoustic waves, in particular the strong convergence of the velocity field.
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