Opttmum Shapes of Bodtes tn Free Surface Flows 
DISCUSSION 
Ernest O. Tuck 
Universtty of Adelatde 
Adelatde, Australta 
At a meeting like this it might seem strange to ask about 
existence and uniqueness solutions to mathematical problems but I 
think it is possibly relevant here. I wondered if the authors know in 
their examples whether they can expect a solution, on either physical 
or mathematical grounds ? 
REPLY TO DISCUSSION 
Arthur K. Whitney 
Palo Alto Research Laboratory, Lockheed Atreraft Corp. 
Pato Alto, Californias U.S.A. 
That is one of the unresolved questions in this minimisation 
technique, we simply do not know the answer at this point. If it turns 
out that solutions to the exact nonlinear equations do not exist, this 
still does not invalidate solutions by the approximate methods. It may 
mean, however, that as we take more and more terms in the appro- 
ximate solutions, these solutions do not converge. An existence proof, 
especially a constructive existence proof, would be very much desi- 
rable. 
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