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Prikladnaya Mekhanika i Tekhnicheskaya Fizika, 2018, Volume 59, Issue 5, Pages 185–190
DOI: https://doi.org/10.15372/PMTF20180521 (Mi pmtf538) 		 
This article is cited in 2 scientific papers (total in 2 papers)

Solving the motion equations of a viscous liquid with a nonlinear dependence between a velocity vector and some spatial variables

D. V. Knyazev

Institute of Continuous Media Mechanics, Ural Branch, Russian Academy of Sciences, 614013, Perm, Russia
Full-text PDF (183 kB) Citations (2)
DOI: https://doi.org/10.15372/PMTF20180521
Abstract: It is shown that the classes of exact solutions of Navier–Stokes equations with a linear and inversely proportional dependence between velocity components and some spatial variables can be expanded by adding finite perturbations, being power or trigonometric series or their sections on one of the coordinates. An example of single integration of three-dimensional equations of motion of a viscous liquid, which are reduced to an equation for the potential of two velocity components, is given.
Keywords: Navier–Stokes equations, exact solutions, separation of variables, overdetermined system.
Received: 12.07.2017
Revised: 28.02.2018
English version:
Journal of Applied Mechanics and Technical Physics, 2018, Volume 59, Issue 5, Pages 928–933
DOI: https://doi.org/10.1134/S0021894418050218
Bibliographic databases:
Document Type: Article
UDC: 532.51
Language: Russian
Citation: D. V. Knyazev, “Solving the motion equations of a viscous liquid with a nonlinear dependence between a velocity vector and some spatial variables”, Prikl. Mekh. Tekh. Fiz., 59:5 (2018), 185–190; J. Appl. Mech. Tech. Phys., 59:5 (2018), 928–933
Citation in format AMSBIB
\Bibitem{Kny18}
\by D.~V.~Knyazev
\paper Solving the motion equations of a viscous liquid with a nonlinear dependence between a velocity vector and some spatial variables
\jour Prikl. Mekh. Tekh. Fiz.
\yr 2018
\vol 59
\issue 5
\pages 185--190
\mathnet{http://mi.mathnet.ru/pmtf538}
\crossref{https://doi.org/10.15372/PMTF20180521}
\elib{https://elibrary.ru/item.asp?id=35606615}
\transl
\jour J. Appl. Mech. Tech. Phys.
\yr 2018
\vol 59
\issue 5
\pages 928--933
\crossref{https://doi.org/10.1134/S0021894418050218}
Linking options:
  • https://www.mathnet.ru/eng/pmtf538
  • https://www.mathnet.ru/eng/pmtf/v59/i5/p185
    • This publication is cited in the following 2 articles:
    1. N. V. Burmasheva, E. Yu. Prosviryakov, “Tochnoe reshenie tipa Kuetta – Puazeilya dlya ustanovivshikhsya kontsentratsionnykh techenii”, Uchen. zap. Kazan. un-ta. Ser. Fiz.-matem. nauki, 164, no. 4, Izd-vo Kazanskogo un-ta, Kazan, 2022, 285–301  mathnet  crossref
    2. V.V. Privalova, E.Y. Prosviryakov, “Nonlinear isobaric flow of a viscous incompressible fluid in a thin layer with permeable boundaries”, Comp. Contin. Mech., 12:2 (2019), 230  crossref
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Prikladnaya Mekhanika i Tekhnicheskaya Fizika Prikladnaya Mekhanika i Tekhnicheskaya Fizika
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