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Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, 2020, Volume 24, Number 4, Pages 762–768
DOI: https://doi.org/10.14498/vsgtu1814 (Mi vsgtu1814) 		 
This article is cited in 3 scientific papers (total in 3 papers)

Short Communication
Mathematical Modelling

A new class of non-helical exact solutions of the Navier–Stokes equations

V. P. Kovaleva, E. Yu. Prosviryakovb

a Moscow Institute of Physics and Technology (National Research University), Dolgoprudny, Moscow region, 141701, Russian Federation
b Institute of Engineering Science, Urals Branch, Russian Academy of Sciences, Ekaterinburg, 620049, Russian Federation
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DOI: https://doi.org/10.14498/vsgtu1814
Abstract: The paper presents a new class of exact solutions for the Navier–Stokes equations. These solutions describe unsteady three-dimensional in velocities and two-dimensional in coordinates for a viscous incompressible fluid flow. The procedure for constructing an exact solution generalizes Trkal's method proposed for studying screw flows. The new class of exact solutions allows to describe non-hecical flows (the velocity vector forms a nonzero angle with the vorticity vector) and fluid flows existing in a finite time.
Keywords: Navier-Stokes equation, exact solution, Trkal's method, eigenfunctions of the Laplacian, non-helical flows, blow-up regimes.
Funding agency Grant number
Russian Science Foundation 19-19-00571
This work was supported by the Russian Science Foundation (project no. 19–19–00571).
Received: July 29, 2020
Revised: September 18, 2020
Accepted: November 16, 2020
First online: December 9, 2020
Bibliographic databases:
Document Type: Article
UDC: 532.517.2
MSC: 76D05, 76D99
Language: English
Citation: V. P. Kovalev, E. Yu. Prosviryakov, “A new class of non-helical exact solutions of the Navier–Stokes equations”, Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 24:4 (2020), 762–768
Citation in format AMSBIB
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\by V.~P.~Kovalev, E.~Yu.~Prosviryakov
\paper A new class of non-helical exact solutions of~the~Navier--Stokes equations
\jour Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.]
\yr 2020
\vol 24
\issue 4
\pages 762--768
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\crossref{https://doi.org/10.14498/vsgtu1814}
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    • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Вестник Самарского государственного технического университета. Серия: Физико-математические науки
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