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Matematicheskie Zametki, 2016, Volume 99, Issue 5, Pages 764–777
DOI: https://doi.org/10.4213/mzm10624 (Mi mzm10624) 		 
This article is cited in 10 scientific papers (total in 10 papers)

On the Homogenization Principle in a Time-Periodic Problem for the Navier–Stokes Equations with Rapidly Oscillating Mass Force

V. L. Khatskevich

Voronezh State University
Full-text PDF (500 kB) Citations (10)
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DOI: https://doi.org/10.4213/mzm10624
Abstract: We study the behavior of the set of time-periodic solutions of the three-dimensional system of Navier–Stokes equations in a bounded domain as the frequency of the oscillations of the right-hand side tends to infinity. It is established that the set of periodic solutions tends to the solution set of the homogenized stationary equation.
Keywords: system of Navier–Stokes equations, homogenization principle, Hilbert space, periodic solution, strong solution.
Received: 08.08.2014
Revised: 19.10.2015
English version:
Mathematical Notes, 2016, Volume 99, Issue 5, Pages 757–768
DOI: https://doi.org/10.1134/S0001434616050138
Bibliographic databases:
Document Type: Article
UDC: 517.9
Language: Russian
Citation: V. L. Khatskevich, “On the Homogenization Principle in a Time-Periodic Problem for the Navier–Stokes Equations with Rapidly Oscillating Mass Force”, Mat. Zametki, 99:5 (2016), 764–777; Math. Notes, 99:5 (2016), 757–768
Citation in format AMSBIB
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    • This publication is cited in the following 10 articles:
    1. V. L. Khatskevich, “On Conditions that Ensure Hydrodynamic Stability and Uniqueness of Stationary and Periodic Liquid Flows”, J Math Sci, 2025  crossref
    2. V. B. Levenshtam, “Usrednenie vysokochastotnoi normalnoi sistemy ODU s mnogotochechnymi kraevymi usloviyami na poluosi”, Izv. vuzov. Matem., 2024, no. 3, 64–69  mathnet  crossref
    3. V. B. Levenshtam, “Averaging of a Normal System of Ordinary Differential Equations of High Frequency with a Multipoint Boundary Value Problem on a Semiaxis”, Russ Math., 68:3 (2024), 53  crossref
    4. V. B. Levenshtam, “Usrednenie abstraktnykh parabolicheskikh uravnenii s mnogotochechnymi integralnymi kraevymi usloviyami”, Vladikavk. matem. zhurn., 26:4 (2024), 95–104  mathnet  crossref
    5. V. B. Levenshtam, “Metod usredneniya dlya kvazilineinoi giperbolicheskoi sistemy. Asimptotika reshenii”, Tr. MMO, 84, no. 1, MTsNMO, M., 2023, 25–35  mathnet
    6. V.B. Levenshtam, “Averaging Method for Quasi-Linear Hyperbolic Systems”, Russ. J. Math. Phys., 30:4 (2023), 552  crossref
    7. Peng Gao, “Averaging principle for multiscale nonautonomous random 2D Navier-Stokes system”, Journal of Functional Analysis, 285:6 (2023), 110036  crossref
    8. V. L. Khatskevich, “Ob uslovii, obespechivayuschem gidrodinamicheskuyu ustoichivost i edinstvennost statsionarnogo i periodicheskogo techenii zhidkosti”, Materialy Voronezhskoi vesennei matematicheskoi shkoly «Sovremennye metody teorii kraevykh zadach. Pontryaginskie chteniya–XXX». Voronezh, 3–9 maya 2019 g. Chast 1, Itogi nauki i tekhn. Sovrem. mat. i ee pril. Temat. obz., 190, VINITI RAN, M., 2021, 122–129  mathnet  crossref
    9. P. Gao, “Averaging principles for the swift-hohenberg equation”, Commun. Pure Appl. Anal, 19:1 (2020), 293–310  crossref  mathscinet  zmath  isi  scopus
    10. V. L. Khatskevich, “Asymptotics of motions of viscous incompressible fluids with large viscosity”, Journal of Mathematical Sciences, 227:4 (2017), 520–530  mathnet  mathnet  crossref
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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