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International Journal of Mathematics and Mathematical Sciences
Volume 30, Issue 5, Pages 283-300

Steady vortex flows obtained from a constrained variational problem

1Department of Mathematics, Iran University of Science and Technology, Narmak, Tehran 16844, Iran
2Institute for Studies in Theoretical Physics and Mathematics, Niavaran Building, Niavaran Square, Tehran, Iran

Received 10 January 2001; Revised 24 August 2001

Copyright © 2002 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We prove the existence of steady two-dimensional ideal vortex flows occupying the first quadrant and containing a bounded vortex; this is done by solving a constrained variational problem. Kinetic energy is maximized subject to the vorticity, being a rearrangement of a prescribed function and subject to a linear constraint.