Regularity of traveling free surface water waves with vorticity

2011/12/12 by Hua Chen, Chen, Hua, Wei-Xi Li +3 · 1 citation
Earth and Planetary Sciences · #Analysis of PDEs (math.AP) #Arctic and Antarctic ice dynamics #Coastal and Marine Dynamics #FOS: Mathematics #Ocean Waves and Remote Sensing

paper · pdf · doi:10.48550/arxiv.1112.2730

openalex publication_date 2011/12/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 Hölder 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.

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