Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika
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Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika, 2022, Number 3, Pages 46–50 (Mi vmumm4475)  

Mechanics

Friedrichs inequalities and sharpened sufficient stability conditions of plane-parallel flows

D. V. Georgievskii

Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
References:
Abstract: From the standpoint of the linearized stability theory, two eigenvalue problems for the Orr–Sommerfeld equation with two groups of boundary conditions having a certain mechanical meaning are considered. On the basis of the integral relations method operating with quadratic functionals, the stability parameter, which is a real part of the spectral parameter, is estimated. The technique of the method involves the application of the Friedrichs inequality for various classes of complex-valued functions. Using the minimizing property of the first positive eigenvalues in the corresponding problems, the values of the constants in some Friedrichs inequalities are increased, which entails the strengthening of the stability sufficient integral estimates for plane-parallel shear flows in a plane layer.
Key words: Orr–Sommerfeld equation, quadratic functional, Friedrichs inequality, spectral parameter, stability, sufficient estimate, minimization.
Received: 20.09.2021
English version:
Moscow University Mechanics Bulletin, 2022, Volume 77, Issue 3, Pages 61–65
DOI: https://doi.org/10.3103/S0027133022030049
Bibliographic databases:
Document Type: Article
UDC: 532.517.3
Language: Russian
Citation: D. V. Georgievskii, “Friedrichs inequalities and sharpened sufficient stability conditions of plane-parallel flows”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2022, no. 3, 46–50; Moscow University Mechanics Bulletin, 77:3 (2022), 61–65
Citation in format AMSBIB
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\by D.~V.~Georgievskii
\paper Friedrichs inequalities and sharpened sufficient stability conditions of plane-parallel flows
\jour Vestnik Moskov. Univ. Ser.~1. Mat. Mekh.
\yr 2022
\issue 3
\pages 46--50
\mathnet{http://mi.mathnet.ru/vmumm4475}
\zmath{https://zbmath.org/?q=an:7604862}
\transl
\jour Moscow University Mechanics Bulletin
\yr 2022
\vol 77
\issue 3
\pages 61--65
\crossref{https://doi.org/10.3103/S0027133022030049}
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