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September  2007, 19(3): 483-491. doi: 10.3934/dcds.2007.19.483

Deep-water waves with vorticity: symmetry and rotational behaviour

Mats Ehrnström 1,

1. 

Centre for Mathematical Sciences, Lund University, PO Box 118, 221 00 Lund, Sweden

Received  May 2007 Revised  July 2007 Published  July 2007

We show that for steady, periodic, and rotational gravity deep-water waves, a monotone surface profile between troughs and crests implies symmetry. It is observed that if the vorticity function has a bounded derivative, then it vanishes as one approaches great depths.
Keywords: nonlinear partial differential equation., Symmetry, water waves, vorticity.
Mathematics Subject Classification: Primary: 76B15, 35Q36; Secondary: 35J25, 35J60, 76B4.
Citation: Mats Ehrnström. Deep-water waves with vorticity: symmetry and rotational behaviour. Discrete & Continuous Dynamical Systems, 2007, 19 (3) : 483-491. doi: 10.3934/dcds.2007.19.483
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