On the dispersion relation for compressible Navier-Stokes Equations

In this paper we revisit the classical sound dispersion and attenuation theory due to Stokes \cite{Stokes}, 1845, and Kirchhoff \cite{Kirchhoff}, 1868, for the propagation of sound in non-ideal fluids. In particular we reformulate the analysis due to Fletcher \cite{Fletcher}, 1974, showing conditions for which the sound propagates at the isothermal speed of sound. Also we presents asymptotic developments making precise the physical conditions under which the different dispersion and attenuation formulas apply. The more complex case of two-fluid flow is addressed by Benjelloun and Ghidaglia \cite{BG} to which the reader is referred.