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An exponential decay estimate for the stationary axisymmetric perturbation of Poiseuille flow in a circular pipe

  • Gerardo A. Ache
Original Papers
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Abstract

We prove a decay estimate for the steady state incompressible Navier-Stokes equations. The estimate describes the exponential decay, in the axial direction of a semi-infinite circular tube, for an energy-type functional in terms of the axisymmetric perturbation of Poiseuille flow, provided that the Reynolds number does not exceed a critical value, for which we exhibit a lower and an upper bound. Since the motion is considered axisymmetric we use a stream function formulation, and the results are similar to those obtained by Horgan [8], for a two-dimensional channel flow problem. For the Stokes problem our estimate for the rate of decay is a lower bound to the actual rate of decay which is obtained from an asymptotic solution to the Stokes equations. Finally we describe a numerical approach to computing bounds to the energy functionalE(0).

Keywords

Reynolds Number Exponential Decay Stream Function Poiseuille Flow Decay Estimate 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Birkhäuser Verlag 1994

Authors and Affiliations

  • Gerardo A. Ache
    • 1
  1. 1.Facultad de CienciasUniversidad Central de Venezuela-CaracasVenezuela

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