SPECTRAL PROPERTIES OF THE ORR-SOMMERFELD PROBLEM

Authors
LANGER H TRETTER C
Citation
H. Langer et C. Tretter, SPECTRAL PROPERTIES OF THE ORR-SOMMERFELD PROBLEM, Proceedings of the Royal Society of Edinburgh. Section A. Mathematics, 127, 1997, pp. 1245-1261
Citations number
8
Categorie Soggetti
Mathematics,Mathematics,Mathematics,Mathematics
Journal title
Proceedings of the Royal Society of Edinburgh. Section A. Mathematics → ACNP
ISSN journal
03082105
Volume
127
Year of publication
1997
Part
6
Pages
1245 - 1261
Database
ISI
SICI code
0308-2105(1997)127:<1245:SPOTOP>2.0.ZU;2-9
Abstract
In this paper, we study the Orr-Sommerfeld problem on a finite interva l. It is shown that the eigenfunctions and associated functions form a Bari basis in a suitable Hilbert space if the unperturbed velocity pr ofile u is sufficiently smooth. To this end, the Orr-Sommerfeld proble m is considered as a bounded perturbation of a certain self-adjoint sp ectral problem.