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Zbl 1080.35065
Bresch, Didier; Gisclon, Marguerite; Lin, Chi-Kun
An example of low Mach (Froude) number effects for compressible flows with nonconstant density (height) limit. (English)
[J] ESAIM, Math. Model. Numer. Anal. 39, No. 3, 477-486 (2005). ISSN 0764-583X; ISSN 1290-3841/e

Summary: The authors 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.

MSC 2000:: *35Q30 Stokes and Navier-Stokes equations
76N10 Compressible fluids, general
76G25 General aerodynamics and subsonic flows
35B40 Asymptotic behavior of solutions of PDE

Keywords: viscous shallow water equation; viscous lake equations; well prepared data; weak solutions

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