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# Accession Number:

## ADA193480

# Title:

## An Exponential Decay Estimate for the Stationary Perturbation of Poiseuille Flow.

# Descriptive Note:

## Technical summary rept.,

# Corporate Author:

## WISCONSIN UNIV-MADISON CENTER FOR MATHEMATICAL SCIENCES

# Report Date:

## 1987-10-01

# Pagination or Media Count:

##
35.0

# Abstract:

## The author proves 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 tube, for an energy-type functional in terms of the 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 axi-symmetric we use a stream function formulation, and the results are similar to those obtained by Horgan 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.

# Distribution Statement:

## APPROVED FOR PUBLIC RELEASE

#