# An example of low Mach (Froude) number effects for compressible flows with nonconstant density (height) limit

Didier Bresch; Marguerite Gisclon; Chi-Kun Lin

- Volume: 39, Issue: 3, page 477-486
- ISSN: 0764-583X

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topBresch, Didier, Gisclon, Marguerite, and 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 39.3 (2005): 477-486. <http://eudml.org/doc/244834>.

@article{Bresch2005,

abstract = {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.},

author = {Bresch, Didier, Gisclon, Marguerite, Lin, Chi-Kun},

journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},

keywords = {compressible flows; Navier-Stokes equations; low Mach (Froude) number limit shallow-water equations; lake equations; nonconstant density; viscous shallow water equation; viscous lake equations; well prepared data; weak solutions},

language = {eng},

number = {3},

pages = {477-486},

publisher = {EDP-Sciences},

title = {An example of low Mach (Froude) number effects for compressible flows with nonconstant density (height) limit},

url = {http://eudml.org/doc/244834},

volume = {39},

year = {2005},

}

TY - JOUR

AU - Bresch, Didier

AU - Gisclon, Marguerite

AU - Lin, Chi-Kun

TI - An example of low Mach (Froude) number effects for compressible flows with nonconstant density (height) limit

JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

PY - 2005

PB - EDP-Sciences

VL - 39

IS - 3

SP - 477

EP - 486

AB - 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.

LA - eng

KW - compressible flows; Navier-Stokes equations; low Mach (Froude) number limit shallow-water equations; lake equations; nonconstant density; viscous shallow water equation; viscous lake equations; well prepared data; weak solutions

UR - http://eudml.org/doc/244834

ER -

## References

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