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Mathematical Notes

, Volume 99, Issue 5–6, pp 636–642 | Cite as

Existence of the stationary solution of a Rayleigh-type equation

  • D. I. Borisov
  • R. K. Gaydukov
Article

Abstract

A fluid flow along a semi-infinite plate with small periodic irregularities on the surface is considered for large Reynolds numbers. The boundary layer has a double-deck structure: a thin boundary layer (“lower deck”) and a classical Prandtl boundary layer (“upper deck”). The aim of this paper is to prove the existence and uniqueness of the stationary solution of a Rayleigh-type equation, which describes oscillations of the vertical velocity component in the classical boundary layer.

Keywords

double-deck structure boundary-layer theory fluid mechanics Navier–Stokes equations Rayleigh-type equation eigenvalue problem 

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Copyright information

© Pleiades Publishing, Ltd. 2016

Authors and Affiliations

  1. 1.Institute of Mathematics with Computer Center, Ufa Scientific CenterRussian Academy of SciencesUfaRussia
  2. 2.Akhmulla Bashkir State Pedagogical UniversityUfaRussia
  3. 3.University of Hrádec KrálovéHrádec KrálovéCzech Republic
  4. 4.National Research University Higher School of EconomicsMoscowRussia

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