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An example of low Mach (Froude) number effects for compressible flows with nonconstant density (height) limit
ESAIM: Mathematical Modelling and Numerical Analysis , Special issue on Low Mach Number Flows Conference, Tome 39 (2005) no. 3, pp. 477-486
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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.

DOI : 10.1051/m2an:2005026
Classification : 35Q30
Keywords: compressible flows, Navier-Stokes equations, low Mach (Froude) number limit shallow-water equations, lake equations, nonconstant density 
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     author = {Bresch, Didier and Gisclon, Marguerite and Lin, Chi-Kun},
     title = {An example of low {Mach} {(Froude)} number effects for compressible flows with nonconstant density (height) limit},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
     pages = {477--486},
     year = {2005},
     publisher = {EDP-Sciences},
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     number = {3},
     doi = {10.1051/m2an:2005026},
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     zbl = {1080.35065},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/m2an:2005026/}
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Bresch, Didier; Gisclon, Marguerite; 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 , Special issue on Low Mach Number Flows Conference, Tome 39 (2005) no. 3, pp. 477-486. doi: 10.1051/m2an:2005026

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