Domain sensitivity in singular limits of compressible viscous fluids

Eduard Feireisl[1]

  • [1] Institute of Mathematics of the Academy of Sciences of the Czech Republic Žitná 25 115 67 Praha 1 Czech Republic

Séminaire Laurent Schwartz — EDP et applications (2011-2012)

  • Volume: 2011-2012, page 1-16
  • ISSN: 2266-0607

Abstract

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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 Ω ⊂ 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.

How to cite

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Feireisl, Eduard. "Domain sensitivity in singular limits of compressible viscous fluids." Séminaire Laurent Schwartz — EDP et applications 2011-2012 (2011-2012): 1-16. <http://eudml.org/doc/251160>.

@article{Feireisl2011-2012,
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.},
affiliation = {Institute of Mathematics of the Academy of Sciences of the Czech Republic Žitná 25 115 67 Praha 1 Czech Republic},
author = {Feireisl, Eduard},
journal = {Séminaire Laurent Schwartz — EDP et applications},
keywords = {compressible viscous barotropic fluid},
language = {eng},
pages = {1-16},
publisher = {Institut des hautes études scientifiques & Centre de mathématiques Laurent Schwartz, École polytechnique},
title = {Domain sensitivity in singular limits of compressible viscous fluids},
url = {http://eudml.org/doc/251160},
volume = {2011-2012},
year = {2011-2012},
}

TY - JOUR
AU - Feireisl, Eduard
TI - Domain sensitivity in singular limits of compressible viscous fluids
JO - Séminaire Laurent Schwartz — EDP et applications
PY - 2011-2012
PB - Institut des hautes études scientifiques & Centre de mathématiques Laurent Schwartz, École polytechnique
VL - 2011-2012
SP - 1
EP - 16
AB - 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.
LA - eng
KW - compressible viscous barotropic fluid
UR - http://eudml.org/doc/251160
ER -

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