An example of low Mach (Froude) number effects for compressible flows with nonconstant density (height) limit
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 39 (2005) no. 3, p. 477-486

The purpose of this work is to study an example of low Mach (Froude) number limit of compressible flows when the initial density (height) is almost equal to a function depending on $x$. This allows us to connect the viscous shallow water equation and the viscous lake equations. More precisely, we study this asymptotic with well prepared data in a periodic domain looking at the influence of the variability of the depth. The result concerns weak solutions. In a second part, we discuss the general low Mach number limit for standard compressible flows given in P.-L. Lions’ book that means with constant viscosity coefficients.

DOI : https://doi.org/10.1051/m2an:2005026
Classification:  35Q30
Keywords: compressible flows, Navier-Stokes equations, low Mach (Froude) number limit shallow-water equations, lake equations, nonconstant density
@article{M2AN_2005__39_3_477_0,
author = {Bresch, Didier and Gisclon, Marguerite and Lin, Chi-Kun},
title = {An example of low Mach (Froude) number effects for compressible flows with nonconstant density (height) limit},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
publisher = {EDP-Sciences},
volume = {39},
number = {3},
year = {2005},
pages = {477-486},
doi = {10.1051/m2an:2005026},
zbl = {1080.35065},
mrnumber = {2157146},
language = {en},
url = {http://www.numdam.org/item/M2AN_2005__39_3_477_0}
}

Bresch, Didier; Gisclon, Marguerite; Lin, Chi-Kun. An example of low Mach (Froude) number effects for compressible flows with nonconstant density (height) limit. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 39 (2005) no. 3, pp. 477-486. doi : 10.1051/m2an:2005026. http://www.numdam.org/item/M2AN_2005__39_3_477_0/

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