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Prikladnaya Mekhanika i Tekhnicheskaya Fizika, 2019, Volume 60, Issue 2, Pages 169–179
DOI: https://doi.org/10.15372/PMTF20190214 (Mi pmtf468) 		 
Crack opening models based the exact solutions of Navier–Stokes equations

S. V. Khabirov, S. S. Khabirov

Mavlyutov Institute of Mechanics, Ufa Investigation Center, Russian Academy of Science, Ufa, 450054, Russia
Full-text PDF (232 kB)
DOI: https://doi.org/10.15372/PMTF20190214
Abstract: Different approximate crack opening models in a porous stratum are derived, based on a priori representations of the crack size, accurate solutions of motion equations of viscous fluid, approximate expressions of the filtering model in the stratum, and approximate expressions of the theory of elasticity of the stratum. The law of conservation of momentum of the fluid in the crack is used to obtain quasilinear parabolic equations, describing the crack opening.
Keywords: crack opening, Navier–Stokes equations, exact solutions, quasilinear parabolic equations.
Funding agency Grant number
Ministry of Education and Science of the Russian Federation 18-29-10071 МК
Ministry of Science and Higher Education of the Russian Federation 0246-2019-0052
Received: 15.11.2018
Revised: 15.11.2018
Accepted: 26.11.2018
English version:
Journal of Applied Mechanics and Technical Physics, 2019, Volume 60, Issue 2, Pages 332–341
DOI: https://doi.org/10.1134/S0021894419020147
Bibliographic databases:
Document Type: Article
UDC: 517.958:532.5
Language: Russian
Citation: S. V. Khabirov, S. S. Khabirov, “Crack opening models based the exact solutions of Navier–Stokes equations”, Prikl. Mekh. Tekh. Fiz., 60:2 (2019), 169–179; J. Appl. Mech. Tech. Phys., 60:2 (2019), 332–341
Citation in format AMSBIB
\Bibitem{KhaKha19}
\by S.~V.~Khabirov, S.~S.~Khabirov
\paper Crack opening models based the exact solutions of Navier--Stokes equations
\jour Prikl. Mekh. Tekh. Fiz.
\yr 2019
\vol 60
\issue 2
\pages 169--179
\mathnet{http://mi.mathnet.ru/pmtf468}
\crossref{https://doi.org/10.15372/PMTF20190214}
\elib{https://elibrary.ru/item.asp?id=37248719}
\transl
\jour J. Appl. Mech. Tech. Phys.
\yr 2019
\vol 60
\issue 2
\pages 332--341
\crossref{https://doi.org/10.1134/S0021894419020147}
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