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Spectral properties of compressible stratified flows

Keywords: partial differential equations, essential spectrum, sobolev spaces, stratified fluid, internal waves.

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Abstract:

for bounded and unbounded domains in r3, we establish the localization and the structure of the spectrum of normal vibrations described by systems of partial differential equations modelling small displacements of compressible stratified fluid in the homogeneous gravity field. we also compare the spectral properties of gravitational and rotational operators. our main result is the construction of weyl sequence for the essential spectrum, which is an explicit form of non-uniqueness of the solutions.

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