Comptes Rendus
no. 1-2
Partial Differential Equations
Well-posedness of a low Mach number system

Presented by: the Editorial Board

Yohan Penel1
1 Commissariat à lʼénergie atomique et aux énergies alternatives, centre de Saclay – DEN/DANS/DM2S/SFME/LETR, 91191 Gif-sur-Yvette, France
Comptes Rendus. Mathématique, Volume 350 (2012) no. 1-2, pp. 51-55.

This Note deals with a short-time existence result for a system of nonlinear partial differential equations modelling a diphasic flow. The so-called Dlmn system is derived from the compressible Navier–Stokes equations under the assumption that the Mach number is small. A classical solution is obtained by means of a Picard iteration process. The proof of convergence relies on estimates associated to hyperbolic and parabolic equations. This procedure results in conditions on the time of existence of the solution.

Cette Note est consacrée à un résultat dʼexistence en temps court dʼune solution classique à un système non-linéaire dʼéquations aux dérivées partielles. Ce système, appelé Dlmn, correspond à lʼordre 0 dans le développement asymptotique à bas nombre de Mach des équations de Navier–Stokes (adimensionnées). Afin de prouver lʼexistence dʼune solution, on construit une suite de type itérées de Picard, dont la convergence repose sur des estimations associées aux équations hyperboliques et paraboliques présentes dans le système. Il en résulte des contraintes portant sur le temps dʼexistence de la solution.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2011.12.009

Yohan Penel 1

1 Commissariat à lʼénergie atomique et aux énergies alternatives, centre de Saclay – DEN/DANS/DM2S/SFME/LETR, 91191 Gif-sur-Yvette, France 
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Yohan Penel. Well-posedness of a low Mach number system. Comptes Rendus. Mathématique, Volume 350 (2012) no. 1-2, pp. 51-55. doi : 10.1016/j.crma.2011.12.009. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2011.12.009/

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