no. 9
Partial differential equations/Mathematical problems in mechanics
Singular limit of a Navier–Stokes system leading to a free/congested zones two-phase model
[Modèle bi-phasique gérant zones libres/zones congestionnées comme limite singulière d'un système de Navier–Stokes compressible]

Présenté par : Jean-Michel Bony

Bresch, Didier1 ; Perrin, Charlotte1 ; Zatorska, Ewelina2, 3
1 Université de Savoie, Laboratoire de mathématiques, UMR CNRS 5127, campus scientifique, 73376 Le Bourget-du-Lac, France
2 Institute of Applied Mathematics and Mechanics, University of Warsaw, ul. Banacha 2, 02-097 Warszawa, Poland
3 CMAP UMR 7641, École polytechnique, CNRS, route de Saclay, 91128 Palaiseau cedex, France
Comptes Rendus. Mathématique, Tome 352 (2014) no. 9, pp. 685-690.

Le but de cette contribution est de justifier mathématiquement l'obtention d'un modèle biphasique visqueux gérant zones libres/zones congestionnées comme limite singulière des équations de Navier–Stokes compressibles barotropes à l'aide d'une pression singulière jouant le rôle d'une barrière. Ce type de systèmes macroscopiques permettant de modéliser le mouvement d'une foule a été proposé dans de nombreux articles. Le lecteur interessé pourra se reporter, par exemple, à la revue de B. Maury [9].

The aim of this work is to justify mathematically the derivation of a viscous free/congested zones two-phase model from the isentropic compressible Navier–Stokes equations with a singular pressure playing the role of a barrier.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2014.06.009
Bresch, Didier 1 ; Perrin, Charlotte 1 ; Zatorska, Ewelina 2, 3

1 Université de Savoie, Laboratoire de mathématiques, UMR CNRS 5127, campus scientifique, 73376 Le Bourget-du-Lac, France
2 Institute of Applied Mathematics and Mechanics, University of Warsaw, ul. Banacha 2, 02-097 Warszawa, Poland
3 CMAP UMR 7641, École polytechnique, CNRS, route de Saclay, 91128 Palaiseau cedex, France 
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Bresch, Didier; Perrin, Charlotte; Zatorska, Ewelina. Singular limit of a Navier–Stokes system leading to a free/congested zones two-phase model. Comptes Rendus. Mathématique, Tome 352 (2014) no. 9, pp. 685-690. doi : 10.1016/j.crma.2014.06.009. http://www.numdam.org/articles/10.1016/j.crma.2014.06.009/

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