Address: Institute of Mathematics of the Polish Academy of Sciences, ul. Śniadeckich 8, 00-656 Warszawa, Poland
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Abstract: We investigate the asymptotic limit of solutions to the Navier-Stokes-Fourier system with the Mach number proportional to a small parameter $\rightarrow 0$, the Froude number proportional to $\sqrt{}$ and when the fluid occupies large domain with spatial obstacle of rough surface varying when $\rightarrow 0$. 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.
AMSclassification: primary 35Q35; secondary 35Q30.
Keywords: Oberbeck-Boussinesq approximation, singular limit, low Mach number, unbounded domain, compressible Navier-Stokes-Fourier system, weak solutions, no-slip boundary condition.
DOI: 10.5817/AM2023-2-231