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

Bresch, Didier; Gisclon, Marguerite; Lin, Chi-Kun

ESAIM: Modélisation mathématique et analyse numérique, Special issue on Low Mach Number Flows Conference, Tome 39 (2005) no. 3, pp. 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.

Classification : 35Q30
Keywords: compressible flows, Navier-Stokes equations, low Mach (Froude) number limit shallow-water equations, lake equations, nonconstant density

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