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Variational formulations for steady water waves with vorticity

Published online by Cambridge University Press:  01 February 2006

ADRIAN CONSTANTIN ,
DAVID SATTINGER  and
WALTER STRAUSS
ADRIAN CONSTANTIN
Affiliation:
Trinity College, Department of Mathematics, Dublin 2, Irelandadrian@maths.tcd.ie
DAVID SATTINGER
Affiliation:
Yale University, Department of Mathematics, New Haven, CT 06520, USAdavid.sattinger@yale.edu
WALTER STRAUSS
Affiliation:
Brown University, Department of Mathematics and Lefschetz Center for Dynamical Systems, Box 1917, Providence, RI 02912, USAwstrauss@math.brown.edu
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Abstract

For free-surface water flows with a vorticity that is monotone with depth, we show that any critical point of a functional representing the total energy of the flow adjusted with a measure of the vorticity, subject to the constraints of fixed mass and horizontal momentum, is a steady water wave.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 548 , 10 February 2006 , pp. 151 - 163
Copyright
© 2006 Cambridge University Press

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