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Vestnik TVGU. Ser. Prikl. Matem. [Herald of Tver State University. Ser. Appl. Math.], 2017, Issue 3, Pages 13–25 (Mi vtpmk176)  

This article is cited in 4 scientific papers (total in 4 papers)

Mathematical Modelling, Numerical Methods and Software Systems

On common exact solutions of Navier-Stokes and quasi-hydrodynamic systems for nonstationary flows

Yu. V. Sheretov

Tver State University, Tver

Abstract: It is shown that the Trkal method for constructing uniformly-helical solutions of nonstationary Navier-Stokes equations is applicable for quasi-hydrodynamic system. A wider class of flows, obeying the generalized Gromeki-Beltrami condition, is considered. Examples of exact solutions, common to the Navier-Stokes and quasi-hydrodynamic systems, but not satisfying the Euler equations, are given.

Keywords: Navier-Stokes and Euler systems, quasi-hydrodynamic equations, exact solutions, Trkal method, generalized Gromeka-Beltrami condition, helical flows.

DOI: https://doi.org/10.26456/vtpmk176

Full text: PDF file (351 kB)
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UDC: 517.95, 532.5
Received: 30.07.2017
Revised: 31.08.2017

Citation: Yu. V. Sheretov, “On common exact solutions of Navier-Stokes and quasi-hydrodynamic systems for nonstationary flows”, Vestnik TVGU. Ser. Prikl. Matem. [Herald of Tver State University. Ser. Appl. Math.], 2017, no. 3, 13–25

Citation in format AMSBIB
\Bibitem{She17}
\by Yu.~V.~Sheretov
\paper On common exact solutions of Navier-Stokes and quasi-hydrodynamic systems for nonstationary flows
\jour Vestnik TVGU. Ser. Prikl. Matem. [Herald of Tver State University. Ser. Appl. Math.]
\yr 2017
\issue 3
\pages 13--25
\mathnet{http://mi.mathnet.ru/vtpmk176}
\crossref{https://doi.org/10.26456/vtpmk176}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Yu. V. Sheretov, “O tochnykh resheniyakh kvazigidrodinamicheskoi sistemy, udovletvoryayuschikh obobschennomu usloviyu Gromeki-Beltrami”, Vestnik TvGU. Seriya: Prikladnaya matematika, 2018, no. 3, 5–18  mathnet  crossref  elib
    2. Yu. V. Sheretov, “Tochnye resheniya kvazigidrodinamicheskoi sistemy na osnove formuly Bio–Savara”, Vestnik TvGU. Seriya: Prikladnaya matematika, 2019, no. 1, 38–49  mathnet  crossref  elib
    3. Yu. V. Sheretov, “O resheniyakh zadachi Koshi dlya kvazigidrodinamicheskoi sistemy”, Vestnik TvGU. Seriya: Prikladnaya matematika, 2020, no. 1, 84–96  mathnet  crossref  elib
    4. Yu. V. Sheretov, “O klassakh tochnykh reshenii kvazigidrodinamicheskoi sistemy”, Vestnik TvGU. Seriya: Prikladnaya matematika, 2020, no. 2, 5–17  mathnet  crossref  elib
  • Vestnik TVGU. Seriya: Prikladnaya Matematika [Herald of Tver State University. Series: Applied Mathematics]
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