In this survey paper, we are concerned with the zero Mach number limit for compressible viscous flows. For the sake of (mathematical) simplicity, we restrict ourselves to the case of barotropic fluids and we assume that the flow evolves in the whole space or satisfies periodic boundary conditions. We focus on the case of ill-prepared data. Hence highly oscillating acoustic waves are likely to propagate through the fluid. We nevertheless state the convergence to the incompressible Navier-Stokes equations when the Mach number goes to . Besides, it is shown that the global existence for the limit equations entails the global existence for the compressible model with small . The reader is referred to [R. Danchin, Ann. Sci. Éc. Norm. Sup. (2002)] for the detailed proof in the whole space case, and to [R. Danchin, Am. J. Math. 124 (2002) 1153-1219] for the case of periodic boundary conditions.
Mots clés : low Mach number limit, compressible Navier-Stokes
@article{M2AN_2005__39_3_459_0,
author = {Danchin, Rapha\"el},
title = {Low {Mach} number limit for viscous compressible flows},
journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique},
pages = {459--475},
publisher = {EDP-Sciences},
volume = {39},
number = {3},
year = {2005},
doi = {10.1051/m2an:2005019},
mrnumber = {2157145},
zbl = {1080.35067},
language = {en},
url = {http://www.numdam.org/articles/10.1051/m2an:2005019/}
}
TY - JOUR AU - Danchin, Raphaël TI - Low Mach number limit for viscous compressible flows JO - ESAIM: Modélisation mathématique et analyse numérique PY - 2005 SP - 459 EP - 475 VL - 39 IS - 3 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/m2an:2005019/ DO - 10.1051/m2an:2005019 LA - en ID - M2AN_2005__39_3_459_0 ER -
%0 Journal Article %A Danchin, Raphaël %T Low Mach number limit for viscous compressible flows %J ESAIM: Modélisation mathématique et analyse numérique %D 2005 %P 459-475 %V 39 %N 3 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/m2an:2005019/ %R 10.1051/m2an:2005019 %G en %F M2AN_2005__39_3_459_0
Danchin, Raphaël. Low Mach number limit for viscous compressible flows. ESAIM: Modélisation mathématique et analyse numérique, Tome 39 (2005) no. 3, pp. 459-475. doi : 10.1051/m2an:2005019. http://www.numdam.org/articles/10.1051/m2an:2005019/
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