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

Levenshtam, V.

doi:10.1090/S1061-0022-2014-01331-3

Justification of the averaging method for a system of equations with the Navier–Stokes operator in the principal part
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by V. B. Levenshtam
Translated by: S. Kislyakov

St. Petersburg Math. J. 26 (2015), 69-90

DOI: https://doi.org/10.1090/S1061-0022-2014-01331-3

Published electronically: November 21, 2014

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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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