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J. Sib. Fed. Univ. Math. Phys., 2013, Volume 6, Issue 3, Pages 308–314 (Mi jsfu316)  

This article is cited in 1 scientific paper (total in 1 paper)

Nonlinear Effects in Poiseuille Problem

Alexander V. Koptev

Makarov State University of Maritime and Inland Shipping, S-Petersburg, Russia

Abstract: Poiseuille problem is the first problem in theoretical hydromechanics for which the exact solution has been found. The solution is a steady state solution of Navier–Stokes equations and it gives the velocity profile known as "Poiseuille parabola". Experimental studies show that parabolic profile occurs very seldom in fluid flows. Usually more complex structures are observed. This fact makes us again focus attention on the problem to obtain other solutions. This paper presents an approach that takes onto consideration all nonlinear terms of Navier–Stokes equations. New solutions of the Poiseuille problem are obtained and their nonlinear properties are identified.

Keywords: partial differential equation, viscous incompressible fluid, nonlinearity, exact solution.

Full text: PDF file (134 kB)
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UDC: 517.958,532.516
Received: 10.01.2013
Received in revised form: 25.02.2013
Accepted: 22.03.2013
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Citation: Alexander V. Koptev, “Nonlinear Effects in Poiseuille Problem”, J. Sib. Fed. Univ. Math. Phys., 6:3 (2013), 308–314

Citation in format AMSBIB
\Bibitem{Kop13}
\by Alexander~V.~Koptev
\paper Nonlinear Effects in Poiseuille Problem
\jour J. Sib. Fed. Univ. Math. Phys.
\yr 2013
\vol 6
\issue 3
\pages 308--314
\mathnet{http://mi.mathnet.ru/jsfu316}


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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. Alexander V. Koptev, “Systematization and analysis of integrals of motion for an incompressible fluid flow”, Zhurn. SFU. Ser. Matem. i fiz., 11:3 (2018), 370–382  mathnet  crossref
  • Журнал Сибирского федерального университета. Серия "Математика и физика"
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