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 J. Sib. Fed. Univ. Math. Phys., 2018, Volume 11, Issue 3, Pages 370–382 (Mi jsfu672)

Systematization and analysis of integrals of motion for an incompressible fluid flow

Alexander V. Koptev

Admiral Makarov State University of Maritime and Inland Shipping, Dvinskaya, 5/7, Saint-Petersburg, 198035, Russia

Abstract: An analysis of integrals of motion of an incompressible fluid flow both known and new obtained by author are presented in the paper. It was found that the known integrals of Lagrange–Cauchy, Bernoulli and Euler–Bernoulli are special cases of a new more general integral. It was shown that the set of all integrals of motion of an incompressible fluid form a logical chain which can be represented as a tree.

Keywords: incompressible fluid, motion, Navier–Stokes equations, Euler equations, partial derivative, root integral, stream pseudo-function, potential, tree.

DOI: https://doi.org/10.17516/1997-1397-2018-11-3-370-382

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Bibliographic databases:

UDC: 517.958:532.516
Accepted: 20.02.2018
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Citation: Alexander V. Koptev, “Systematization and analysis of integrals of motion for an incompressible fluid flow”, J. Sib. Fed. Univ. Math. Phys., 11:3 (2018), 370–382

Citation in format AMSBIB
\Bibitem{Kop18} \by Alexander~V.~Koptev \paper Systematization and analysis of integrals of motion for an incompressible fluid flow \jour J. Sib. Fed. Univ. Math. Phys. \yr 2018 \vol 11 \issue 3 \pages 370--382 \mathnet{http://mi.mathnet.ru/jsfu672} \crossref{https://doi.org/10.17516/1997-1397-2018-11-3-370-382} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000442257300007}