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Zh. Vychisl. Mat. Mat. Fiz., 2013, Volume 53, Number 11, Pages 1903–1922 (Mi zvmmf9950)  

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

Nonlinear stability of a parabolic velocity profile in a plane periodic channel

O. V. Troshkin

Institute for Computer-Aided Design, Russian Academy of Sciences, Vtoraya Brestskaya ul. 19/18, Moscow, 123056, Russia

Abstract: An inviscid or viscous incompressible flow with a general parabolic velocity profile in an infinite plane periodic channel with parallel walls that can move is considered with the impermeability conditions (for the Euler equations) or the no-slip conditions (for the Navier–Stokes equations). The nonlinear (for the original equations) and nonlocal (for all Reynolds numbers) stability of the unperturbed flow with respect to arbitrary two-dimensional smooth perturbations of the initial velocity field is established.

Key words: plane Poiseuille and Couette flows, nonlinear stability.

DOI: https://doi.org/10.7868/S0044466913110148

Full text: PDF file (369 kB)
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English version:
Computational Mathematics and Mathematical Physics, 2013, 53:11, 1729–1747

Bibliographic databases:

UDC: 519.634
Received: 28.11.2012
Revised: 17.01.2013

Citation: O. V. Troshkin, “Nonlinear stability of a parabolic velocity profile in a plane periodic channel”, Zh. Vychisl. Mat. Mat. Fiz., 53:11 (2013), 1903–1922; Comput. Math. Math. Phys., 53:11 (2013), 1729–1747

Citation in format AMSBIB
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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. S. V. Fortova, “Comparative analysis of eddy cascade formation in various turbulent problems”, Comput. Math. Math. Phys., 55:2 (2015), 298–304  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    2. M. S. Belotserkovskaya, O. M. Belotserkovskii, V. V. Denisenko, I. V. Eriklintsev, S. A. Kozlov, E. I. Oparina, O. V. Troshkin, “On the short-wave nature of Richtmyer–Meshkov instability”, Comput. Math. Math. Phys., 56:6 (2016), 1075–1085  mathnet  crossref  crossref  isi  elib
    3. O. V. Troshkin, “Stability theory for a two-dimensional channel”, Comput. Math. Math. Phys., 57:8 (2017), 1320–1334  mathnet  crossref  crossref  isi  elib
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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