Recent results on the incompressible limit

Isabelle Gallagher

Séminaire Bourbaki (2003-2004)

  • Volume: 46, page 29-58
  • ISSN: 0303-1179

Abstract

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In the last two decades, a great amount of progress has been made in the understanding of the passage from the equations governing compressible fluids, to the incompressible equations. The aim of this talk is to present the evolution of the mathematical methods used to study that limit, from the works of S. Klainerman and A. Majda in the eighties, to the recent studies of G. Métivier and S. Schochet (for the non isentropic equations). The methods followed are different according to the initial conditions as well as the boundary conditions; we will describe methods of geometrical optics as well as others linked to the theory of defect measures, Strichartz estimates, and also small divisor type computations.

How to cite

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Gallagher, Isabelle. "Résultats récents sur la limite incompressible." Séminaire Bourbaki 46 (2003-2004): 29-58. <http://eudml.org/doc/252163>.

@article{Gallagher2003-2004,
abstract = {La compréhension du passage des équations de la mécanique des fluides compressibles aux équations incompressibles a fait de grands progrès ces vingt dernières années. L’objectif de cet exposé est de présenter l’évolution des méthodes mathématiques mises en œuvre pour étudier ce passage à la limite, depuis les travaux de S. Klainerman et A. Majda dans les années quatre–vingts, jusqu’à ceux récents de G. Métivier et S. Schochet (pour les équations non isentropiques). Suivant les conditions initiales et les conditions aux bords, les méthodes utilisées sont variées, et nous décrirons des résultats de type optique géométrique aussi bien que d’autres liés à la théorie des mesures de défaut, à des estimations de Strichartz ou encore à des calculs de petits diviseurs.},
author = {Gallagher, Isabelle},
journal = {Séminaire Bourbaki},
keywords = {incompressible limit; oscillations; dispersion; defect measures},
language = {fre},
pages = {29-58},
publisher = {Association des amis de Nicolas Bourbaki, Société mathématique de France},
title = {Résultats récents sur la limite incompressible},
url = {http://eudml.org/doc/252163},
volume = {46},
year = {2003-2004},
}

TY - JOUR
AU - Gallagher, Isabelle
TI - Résultats récents sur la limite incompressible
JO - Séminaire Bourbaki
PY - 2003-2004
PB - Association des amis de Nicolas Bourbaki, Société mathématique de France
VL - 46
SP - 29
EP - 58
AB - La compréhension du passage des équations de la mécanique des fluides compressibles aux équations incompressibles a fait de grands progrès ces vingt dernières années. L’objectif de cet exposé est de présenter l’évolution des méthodes mathématiques mises en œuvre pour étudier ce passage à la limite, depuis les travaux de S. Klainerman et A. Majda dans les années quatre–vingts, jusqu’à ceux récents de G. Métivier et S. Schochet (pour les équations non isentropiques). Suivant les conditions initiales et les conditions aux bords, les méthodes utilisées sont variées, et nous décrirons des résultats de type optique géométrique aussi bien que d’autres liés à la théorie des mesures de défaut, à des estimations de Strichartz ou encore à des calculs de petits diviseurs.
LA - fre
KW - incompressible limit; oscillations; dispersion; defect measures
UR - http://eudml.org/doc/252163
ER -

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