An example of low Mach (Froude) number effects for compressible flows with nonconstant density (height) limit
LMC-IMAG, (CNRS, INPG, UJF, INRIA)
38051 Grenoble Cedex, France. email@example.com
2 Université de Savoie, LAMA, UMR CNRS 5127, 73376 Le Bourget-du-lac, France. firstname.lastname@example.org
3 Department of Mathematics, National Cheng Kung University, Tianan 701 Taiwan. email@example.com
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.
Mathematics Subject Classification: 35Q30
Key words: Compressible flows / Navier-Stokes equations / low Mach (Froude) Number limit shallow-water equations / lake equations / nonconstant density.
© EDP Sciences, SMAI, 2005