Abstract
We study small motions and free oscillations of a compressible stratified liquid, the structure of the spectrum, and the basis property of a system of eigenvectors and obtain asymptotic relations for eigenvalues.
Similar content being viewed by others
References
L. M. Brekhovskikh and V. V. Goncharov, Introduction to Continuum Mechanics [in Russian], Nauka, Moscow (1982).
N. D. Kopachevskii, S. N. Krein, and Ngo Zui Kan, Operator Methods in Linear Hydrodynamics: Evolution and Spectral Problems [in Russian], Nauka, Moscow (1989).
A. S. Markus, Introduction to the Spectral Theory of Polynomial Operator Bundles [in Russian], Shtiintsa, Kishinev (1986).
N. D. Kopachevskii and M. Yu. Tsar’kov, “On the problem of the spectrum of the buoyancy operator,” Zh. Vychisl. Mat. Mat. Fiz., No. 3, 548–551 (1987).
T. A. Suslina, Asymptotics of the Spectrum of Some Problems Related to Oscillations of Liquids [in Russian], Dep. in VINITI, No. 8058-V, Leningrad (1985).
M. V. Keldysh, “On the completeness of eigenfunctions of some classes of nonself-adjoint linear operators,” Usp. Mat. Nauk, 24, Issue 4 (160), 15–41 (1971).
Author information
Authors and Affiliations
Additional information
__________
Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 58, No. 10, pp. 1326–1334, October, 2006.
Rights and permissions
About this article
Cite this article
Vronskii, B.M. On small motions of a “liquid-gas” system in a bounded domain. Ukr Math J 58, 1501–1511 (2006). https://doi.org/10.1007/s11253-006-0149-7
Received:
Issue Date:
DOI: https://doi.org/10.1007/s11253-006-0149-7