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Séminaire Laurent Schwartz — EDP et applications

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Eduard Feireisl
Domain sensitivity in singular limits of compressible viscous fluids
Séminaire Laurent Schwartz — EDP et applications (2011-2012), Exp. No. 12, 16 p., doi: 10.5802/slsedp.9
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Résumé - Abstract

In this note, we discuss several recently developed methods for studying stability of a singular limit process with respect to the shape of the underlying physical space. As a model example, we consider a compressible viscous barotropic fluid occupying a spatial domain $\Omega \subset R^3$. In what follows, we describe two rather different problems: (i) the choice of effective boundary conditions; (ii) the fluid flow in the low Mach number regime. In the remaining part of the paper, we analyze these two issues simultaneously comparing the impact of different scales on the form of the resulting effective equations as well as the boundary conditions. Such a “synthesis” of several mathematical techniques may be useful in analyzing much broader class of multiscale problems.

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