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The Spectrum of a Parametrized Partial Differential Operator Occurring in Hydrodynamics |
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| Authors: | Denk, R. Moller, M. Tretter, C. |
| Affiliation: | NWF I – Mathematik, University of Regensburg D-93040 Regensburg, Germany, robert.denk{at}mathematik.uni-regensburg.de Department of Mathematics, University of the Witwatersrand 2050 WITS, South Africa, 036man{at}cosmos.wits.ac.za Department of Mathematics and Computer Science, University of Leicester University Road, Leicester LE1 7RH, c.tretter{at}mcs.le.ac.uk |
| Abstract: | A partial differential operator associated with natural oscillationsof an incompressible fluid in the neighbourhood of an ellipticalflow is considered. The differentiation is only taken with respectto the angular variable, and thus the operator becomes a familyof ordinary differential operators parametrized by the radialvariable. It is shown that the spectra of these ordinary differentialoperators completely determine the spectrum of the given operatorwhich turns out to have a kind of skeleton structure. |
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