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Journal of the London Mathematical Society 2002 65(2):483-492; doi:10.1112/S0024610701002964
© 2002 by London Mathematical Society
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© The London Mathematical Society

The Spectrum of a Parametrized Partial Differential Operator Occurring in Hydrodynamics

R. Denk, M. Möller and C. Tretter

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

Received 14 March 2001. Revision received 3 July 2001.

A partial differential operator associated with natural oscillations of an incompressible fluid in the neighbourhood of an elliptical flow is considered. The differentiation is only taken with respect to the angular variable, and thus the operator becomes a family of ordinary differential operators parametrized by the radial variable. It is shown that the spectra of these ordinary differential operators completely determine the spectrum of the given operator which turns out to have a kind of skeleton structure.


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