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Prikladnaya Mekhanika i Tekhnicheskaya Fizika, 2022, Volume 63, Issue 3, Pages 14–24
DOI: https://doi.org/10.15372/PMTF20220302 (Mi pmtf47) 		 
This article is cited in 1 scientific paper (total in 1 paper)

Viscous fluid flow in a layer with a free boundary

E. N. Zhuravlevaab

a Institute of Hydrodynamics, Siberian Branch, Russian Academy of Sciences, 630090, Novosibirsk, Russia
b Novosibirsk State University, 630090, Novosibirsk, Russia
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DOI: https://doi.org/10.15372/PMTF20220302
Abstract: A partially invariant solution of a three-dimensional problem with a free boundary for the Navier–Stokes equations is studied. The flow domain under consideration is a horizontal layer bounded by a solid plane from below and by a flat free surface from above. The vertical velocity and pressure are independent of the $x$ and $y$ coordinates. Three flow modes can be formed for different initial velocities of the flow: stabilization to the quiescent state with time, solution blow up within a finite time, and self-similar regime in which the layer thickness unboundedly increases with time.
Keywords: Navier–Stokes equations, problems with a free boundary, self-similar solution, solution blow up.
Funding agency Grant number
Russian Foundation for Basic Research 19-01-00096
Received: 12.05.2021
Revised: 12.05.2021
Accepted: 31.05.2021
English version:
Journal of Applied Mechanics and Technical Physics, 2022, Volume 63, Issue 3, Pages 383–391
DOI: https://doi.org/10.1134/S0021894422030026
Bibliographic databases:
Document Type: Article
UDC: 532.51
Language: Russian
Citation: E. N. Zhuravleva, “Viscous fluid flow in a layer with a free boundary”, Prikl. Mekh. Tekh. Fiz., 63:3 (2022), 14–24; J. Appl. Mech. Tech. Phys., 63:3 (2022), 383–391
Citation in format AMSBIB
\Bibitem{Zhu22}
\by E.~N.~Zhuravleva
\paper Viscous fluid flow in a layer with a free boundary
\jour Prikl. Mekh. Tekh. Fiz.
\yr 2022
\vol 63
\issue 3
\pages 14--24
\mathnet{http://mi.mathnet.ru/pmtf47}
\crossref{https://doi.org/10.15372/PMTF20220302}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4481003}
\elib{https://elibrary.ru/item.asp?id=48659592}
\transl
\jour J. Appl. Mech. Tech. Phys.
\yr 2022
\vol 63
\issue 3
\pages 383--391
\crossref{https://doi.org/10.1134/S0021894422030026}
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    		Prikladnaya Mekhanika i Tekhnicheskaya Fizika Prikladnaya Mekhanika i Tekhnicheskaya Fizika
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    References:7
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