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.
