ON THE SPECTRAL PROPERTIES OF INCOMPRESSIBLE ROTATING STRATIFIED FLUID

We investigate the structure and localization of the spectrum of normal vibrations for rotating exponentially stratified incompressible fluid in bounded three-dimensional domains. We prove that all the spectrum is essential, and it is represented by an interval of the imaginary axis which is symmetrical with respect to zero. The obtained results may find their application in the models of the atmosphere and the Ocean which consider the rotation of the Earth over the vertical axis. The novelty of this research is to extend our previous results to the case of the incompressible fluid.