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Justification of the averaging method for a system of equations with the Navier-Stokes operator in the principal part


Author: V. B. Levenshtam
Translated by: S. Kislyakov
Original publication: Algebra i Analiz, tom 26 (2014), nomer 1.
Journal: St. Petersburg Math. J. 26 (2015), 69-90
MSC (2010): Primary 35Q30
DOI: https://doi.org/10.1090/S1061-0022-2014-01331-3
Published electronically: November 21, 2014
MathSciNet review: 3234805
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Abstract | References | Similar Articles | Additional Information

Abstract: The averaging method is justified for a system of partial differential equations with the Navier-Stokes operator in the principal part. The right-hand side of this system (an analog of a mass force) oscillates in time with frequency $ \omega \gg 1$, depends polynomially on the unknown (an analog of the flow velocity), and involves a linear summand proportional to $ \sqrt {\omega }$. An initial-boundary value problem and a problem on time-periodic solutions are considered.


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Additional Information

V. B. Levenshtam
Affiliation: Southern Federal University, ul. Mil′chakova 8-a, Rostov-on-Don 344090, Russia
Email: vleven@math.rsu.ru

DOI: https://doi.org/10.1090/S1061-0022-2014-01331-3
Keywords: Partial differential equations, Navier--Stokes operator, rapidly oscillating summands, averaging method
Received by editor(s): August 15, 2012
Published electronically: November 21, 2014
Article copyright: © Copyright 2014 American Mathematical Society