Steady water waves with multiple critical layers

Details Steady water waves with multiple critical layers Steady water waves with multiple critical layers

2010-04-29

arxiv.org/abs/1004.5227v2

Mathematics

Analysis of PDEs

16 pages, 2 figures. As accepted for publication in SIAM J. Math. Anal

Scientific paper

We construct small-amplitude periodic water waves with multiple critical
layers. In addition to waves with arbitrarily many critical layers and a single
crest in each period, two-dimensional sets of waves with several crests and
troughs in each period are found. The setting is that of steady two-dimensional
finite-depth gravity water waves with vorticity.

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