| Contents |
| We will present the asymptotic analysis of solutions to the compressible Navier-Stokes-Fourier system, when the Mach number is small proportional to $\epsilon$, Froud number is proportional to $\sqrt{\epsilon}$ and $\epsilon \to 0$ and the domain containing the fluid varies with changing parameter $\epsilon$. In particular, the fluid is driven by a gravitation generated by object(s) placed in the fluid of diameter converging to zero. As $\epsilon \to 0$, we will show that the fluid velocity converges to
a solenoidal vector field satisfying the Oberbeck-Boussinesq approximation on ${R}^3$ space with a concentric gravitation force.
The proof is based on the spectral analysis of the associated wave propagator (Neumann Laplacian) governing the motion of acoustic waves.\\[2ex]
{\it References}
\begin{itemize}
\item[{[1]}] A.~Wr\'oblewska-Kami\'nska. Asymptotic analysis of complete fluid system on varying domain: from compressible to incompressible flow. Preprint on http://mmns.mimuw.edu.pl/preprints.html.
\item[{[2]}] E. Feireisl, T. Karper, O. Kreml, J. Stebel. Stability with respect to domain of the low Mach number limit of compressible viscous fluids. {\it M3AS}, 23(13):2465-2493, 2013.
\item[{[3]}] E.~Feireisl, M.~Schonbek.
On the Oberbeck-Boussinesq approximation on unbounded domains.
{\it Nonlinear partial differential equations}, edited by: H.Holden, K.H.Karlsen, Abel Symposial, vol. 7, Springer, Berlin, 2012.
\item[{[4]}] E. Feireisl. Local decay of acoustic waves in the low mach number limits on
general unbounded domains under slip boundary conditions.
{\it Commun. Partial Differential Equations} 36,1778-1796, 2011.
\end{itemize} |
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