Abstract
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 language | English |
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Pages (from-to) | 477-486 |
Number of pages | 10 |
Journal | Mathematical Modelling and Numerical Analysis |
Volume | 39 |
Issue number | 3 |
DOIs | |
Publication status | Published - May 2005 |
Externally published | Yes |
Keywords
- Compressible flows
- Lake equations
- Low Mach (Froude) number limit shallow-water equations
- Navier-Stokes equations
- Nonconstant density