[Caractère bien posé dʼun modèle bas Mach]
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.
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.
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@article{CRMATH_2012__350_1-2_51_0,
author = {Penel, Yohan},
title = {Well-posedness of a low {Mach} number system},
journal = {Comptes Rendus. Math\'ematique},
pages = {51--55},
publisher = {Elsevier},
volume = {350},
number = {1-2},
year = {2012},
doi = {10.1016/j.crma.2011.12.009},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2011.12.009/}
}
TY - JOUR AU - Penel, Yohan TI - Well-posedness of a low Mach number system JO - Comptes Rendus. Mathématique PY - 2012 SP - 51 EP - 55 VL - 350 IS - 1-2 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2011.12.009/ DO - 10.1016/j.crma.2011.12.009 LA - en ID - CRMATH_2012__350_1-2_51_0 ER -
Penel, Yohan. Well-posedness of a low Mach number system. Comptes Rendus. Mathématique, Tome 350 (2012) no. 1-2, pp. 51-55. doi : 10.1016/j.crma.2011.12.009. http://www.numdam.org/articles/10.1016/j.crma.2011.12.009/
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