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Article overview
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Regularity of traveling free surface water waves with vorticity | | Wei-Xi Li
; Ling-Jun Wang
; | | Date: |
12 Dec 2011 | | Abstract: | We prove real analyticity of all the streamlines, including the free surface,
of a gravity- or capillary-gravity-driven steady flow of water over a flat bed,
with a H"{o}lder continuous vorticity function, provided that the propagating
speed of the wave on the free surface exceeds the horizontal fluid velocity
throughout the flow. Furthermore, if the vorticity possesses some Gevrey
regularity of index $s$, then the stream function admits the same Gevrey
regularity throughout the fluid domain; in particular if the Gevrey index $s$
equals to 1, then we obtain analyticity of the stream function. The regularity
results hold for both periodic and solitary water waves. | | Source: | arXiv, 1112.2730 | | Services: | Forum | Review | PDF | Favorites | |
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