Spectral Properties of Normal Vibrations in a Viscous Compressible Barotropic Stratified Fluid

摘要

We study the structure and the localization of the spectrum for the problems modelling the inner oscillations of viscous compressible barotropic stratified three-dimensional fluid. We prove that the essential spectrum consists of three real isolated points which depend on the boundary conditions. We find the sector of the complex plane to which all the eigenvalues belong. We consider both the viscous fluid and the inviscid fluid. Since the model of an exponentially decreasing initial density with the growth of the altitude corresponds to the Boltzmann normal distribution in a homogeneous gravitational field, the results of this paper may find their application in the study of the Ocean and the Atmosphere of the Earth.