Communications in Mathematical Sciences

Volume 10 (2012)

Number 1

Special Issue on the Occasion of C. David Levermore’s Sixtieth Birthday

Asymptotic analysis of acoustic waves in a porous medium: initial layers in time

Pages: 239 – 265



Jose Diaz-Alban (Courant Institute, New York University, New York)

Nader Masmoudi (Courant Institute, New York University, New York)


This is the first of a series of three papers which study acoustic waves governed by the linearized compressible Navier-Stokes equations in a porous medium. In particular, we want to analyze the simultaneous inviscid and high frequency limits of fluid flows in a porous medium. In this paper, we focus on the case of strongly viscous flow, namely fluid flow without the presence of boundary layers in space. We study the behavior of the energy using two-scale expansions in space and reveal that initial layers in time trap the energy carried by the flow during the usual two-scale homogenization process. We examine the time-space boundary layer problem in our forthcoming works.


acoustic waves, compressible Navier-Stokes, porous medium, boundary layers

2010 Mathematics Subject Classification

35B27, 35B40, 76M50, 76N20

Published 14 October 2011