| Issue |
ESAIM: M2AN
Volume 39, Number 3, May-June 2005
Special issue on Low Mach Number Flows Conference
|
|
|---|---|---|
| Page(s) | 477 - 486 | |
| DOI | https://doi.org/10.1051/m2an:2005026 | |
| Published online | 15 June 2005 | |
An example of low Mach (Froude) number effects for compressible flows with nonconstant density (height) limit
1
LMC-IMAG, (CNRS, INPG, UJF, INRIA)
38051 Grenoble Cedex, France. didier.bresch@imag.fr
2
Université de Savoie,
LAMA, UMR CNRS 5127, 73376 Le Bourget-du-lac, France.
marguerite.gisclon@univ-savoie.fr
3
Department of Mathematics,
National Cheng Kung University, Tianan 701 Taiwan.
cklin@mail.ncku.edu.tw
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.
Mathematics Subject Classification: 35Q30
Key words: Compressible flows / Navier-Stokes equations / low Mach (Froude) Number limit shallow-water equations / lake equations / nonconstant density.
© EDP Sciences, SMAI, 2005
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