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# Accession Number:

## ADA114489

# Title:

## On the Swirling Flow between Rotating Coaxial Disks: Existence and Nonuniqueness.

# Descriptive Note:

## Technical summary rept.,

# Corporate Author:

## WISCONSIN UNIV-MADISON MATHEMATICS RESEARCH CENTER

# Report Date:

## 1982-01-01

# Pagination or Media Count:

##
43.0

# Abstract:

## Consider solutions Gx,epsilon, Hx,epsilon of the von Karman equations for the swirling flow between two rotating coaxial disks 1.1 epsilonH superscript iv HH GG equal 0 and 1.2 epsilonG HG - HG equal 0 with boundary conditions 1.3 H0,epsilon equal H 0,epsilon equal H1, epsilon equal H1, epsilon equal 0 1.4 G0, epsilon equal s, G1, epsilon equal 1, s 1. In this work we establish the existence of solutions for epsilon small enough. In fact, if n is a given positive integer with sign s equal -1 to the n power then there is - for epsilon greater than 0 sufficiently small - a solution with the additional property Gx, epsilon has n interior zeros. If n 1 there are at least two such solutions. If s equal 0 there is at least one such solution for every positive integer n. The asymptotic shape of these solutions is described.

# Distribution Statement:

## APPROVED FOR PUBLIC RELEASE

#