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Keywords:
Oberbeck-Boussinesq approximation; singular limit; low Mach number; unbounded domain; compressible Navier-Stokes-Fourier system; weak solutions; no-slip boundary condition
Oberbeck-Boussinesq approximation; singular limit; low Mach number; unbounded domain; compressible Navier-Stokes-Fourier system; weak solutions; no-slip boundary condition
Summary:
We investigate the asymptotic limit of solutions to the Navier-Stokes-Fourier system with the Mach number proportional to a small parameter $\varepsilon \rightarrow 0$, the Froude number proportional to $\sqrt{\varepsilon}$ and when the fluid occupies large domain with spatial obstacle of rough surface varying when $\varepsilon\rightarrow 0$. 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.
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