Vibrations of viscous compressible fluid in bounded domains: spectral properties and asymptotics

In this paper we consider the equations of small (acoustic) vibrations of a viscous compressible barotropic fluid in a bounded smooth domain under different boundary conditions. The structure of the spectrum is investigated; the estimates of the norm of the resolvent operator of the forced vibration problems are presented; the infinite asymptotic expansions of eigenfrequencies and eigenfunctions in series in a vanishing viscosity coefficient are obtained; the leading terms of these expansions are determined analytically.