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

Didier Bresch*, Marguerite Gisclon, Chi Kun Lin

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

17 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)477-486
Number of pages10
JournalMathematical Modelling and Numerical Analysis
Issue number3
Publication statusPublished - May 2005
Externally publishedYes


  • Compressible flows
  • Lake equations
  • Low Mach (Froude) number limit shallow-water equations
  • Navier-Stokes equations
  • Nonconstant density

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