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

Didier Bresch; Marguerite Gisclon; Chi-Kun Lin

ESAIM: Mathematical Modelling and Numerical Analysis (2010)

- 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 39.3 (2010): 477-486. <http://eudml.org/doc/194271>.

@article{Bresch2010,

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},

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},

month = {3},

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/194271},

volume = {39},

year = {2010},

}

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

DA - 2010/3//

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/194271

ER -

## References

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