Introduction to Ideal Fluid Flows

2009 ◽  
pp. 17-27
Keyword(s):  
Ideal Fluid ◽  
Fluid Flows

Maximisation and minimisation on classes of rearrangements

1991 ◽  
Vol 119 (3-4) ◽  
pp. 287-300 ◽  
Author(s):  
G. R. Burton ◽  
J. B. McLeod
Keyword(s):  
Angular Momentum ◽  
Finite Number ◽  
Bounded Domain ◽  
Ideal Fluid ◽  
Fluid Flows ◽  
Linear Constraints ◽  
Dirichlet Integral ◽  
The One

SynopsisMaximisation and minimisation of the Dirichlet integral of a function vanishing on the boundary of a bounded domain are studied, subject to the constraint that the Laplacean be a rearrangement of a given function. When the Laplacean is two-signed, non-existence of minimisers is proved, and some information on the limits of minimising sequences obtained; this contrasts with the known existence of minimisers in the one-signed case. When the domain is a ball and the Laplacean is one-signed, maximisers and minimisers are shown to be radial and monotone. Existence of maximisers is proved subject additionally to a finite number of linear constraints, with particular reference to ideal fluid flows of prescribed angular momentum in a disc.

Harmonic Maps and Ideal Fluid Flows

2011 ◽  
Vol 204 (2) ◽  
pp. 479-513 ◽  
Author(s):  
A. Aleman ◽  
A. Constantin
Keyword(s):  
Ideal Fluid ◽  
Harmonic Maps ◽  
Fluid Flows

Free-Surface Ideal Fluid Flows by Finite Elements

1973 ◽  
Vol 99 (6) ◽  
pp. 959-974
Author(s):  
Stevens T. K. Chan ◽  
Bruce E. Larock ◽  
Leonard R. Herrmann
Keyword(s):  
Free Surface ◽  
Finite Elements ◽  
Ideal Fluid ◽  
Fluid Flows
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