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Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.]:
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Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 2020, Volume 24, Number 2, Pages 319–330 (Mi vsgtu1766)  

This article is cited in 3 scientific papers (total in 3 papers)

Mathematical Modeling, Numerical Methods and Software Complexes

Exact solutions to generalized plane BeltramiTrkal and Ballabh flows

E. Yu. Prosviryakov

Institute of Engineering Science, Urals Branch, Russian Academy of Sciences, Ekaterinburg, 620049, Russian Federation

Abstract: Nonstationary plane flows of a viscous incompressible fluid in a potential field of external forces are considered. An elliptic partial differential equation is obtained, with each solution being a vortex flow stream function described by an exact solution to the NavierStokes equations. The obtained solutions generalize the BeltramiTrkal and Ballabh flows. Examples of such new solutions are given. They are intended to verify numerical algorithms and computer programs.

Keywords: exact solutions to the NavierStokes equations, BeltramiTrkal flow, Ballabh flow

DOI: https://doi.org/10.14498/vsgtu1766

Full text: PDF file (3571 kB) (published under the terms of the Creative Commons Attribution 4.0 International License)
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Bibliographic databases:

UDC: 532.511, 517.958:531.3-324
MSC: 76F02, 76M45, 76F45, 76R05, 76U05
Received: January 7, 2020
Revised: February 27, 2020
Accepted: March 16, 2020
First online: June 16, 2020
Language:

Citation: E. Yu. Prosviryakov, “Exact solutions to generalized plane BeltramiTrkal and Ballabh flows”, Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 24:2 (2020), 319–330

Citation in format AMSBIB
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\by E.~Yu.~Prosviryakov
\paper Exact solutions to generalized plane BeltramiTrkal and~Ballabh flows
\jour Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.]
\yr 2020
\vol 24
\issue 2
\pages 319--330
\mathnet{http://mi.mathnet.ru/vsgtu1766}
\crossref{https://doi.org/10.14498/vsgtu1766}
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. G. B. Sizykh, “Metod tirazhirovaniya tochnykh reshenii uravnenii Eilera dlya neszhimaemykh techenii Beltrami”, Vestn. Sam. gos. tekhn. un-ta. Ser. Fiz.-mat. nauki, 24:4 (2020), 790–798  mathnet  crossref  elib
    2. V. P. Kovalev, E. Yu. Prosviryakov, “A new class of non-helical exact solutions of the Navier–Stokes equations”, Vestn. Sam. gos. tekhn. un-ta. Ser. Fiz.-mat. nauki, 24:4 (2020), 762–768  mathnet  crossref  elib
    3. I. Yu. Mironyuk, L. A. Usov, “Invariant linii tormozheniya pri statsionarnom obtekanii tela zavikhrennym potokom idealnoi neszhimaemoi zhidkosti”, Vestn. Sam. gos. tekhn. un-ta. Ser. Fiz.-mat. nauki, 24:4 (2020), 780–789  mathnet  crossref  elib
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