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Spectral properties of the Orr-Sommerfeld problem

Published online by Cambridge University Press:  14 November 2011

Heinz Langer  and
Christiane Tretter
Heinz Langer
Affiliation:
Institut für Analysis, Technische Mathematik und Versicherungsmathematik, Technische Universität Wien, Wiedner Hauptstr. 8-10, A-1040 Wien, Austria
Christiane Tretter
Affiliation:
NWF I—Mathematik, Universität Regensburg, D-93040 Regensburg, Germany
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Extract

In this paper, we study the Orr–Sommerfeld problem on a finite interval. It is shown that the eigenfunctions and associated functions form a Bari basis in a suitable Hilbert space if the unperturbed velocity profile u is sufficiently smooth. To this end, the Orr–Sommerfeld problem is considered as a bounded perturbation of a certain self-adjoint spectral problem.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 127 , Issue 6 , 1997 , pp. 1245 - 1261
Copyright
Copyright © Royal Society of Edinburgh 1997

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