Analyticity of rotational flows beneath solitary water waves

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Real analyticity of streamlines is established of a gravity-driven steady flow of water in a two-dimensional channel enclosed by a supercritical solitary wave on the free surface and a rigid flat bed, for an arbitrary Hölder continuous vorticity, provided that the wave speed exceeds the horizontal fluid velocity throughout the flow. On the basis of the formulation of the solitary water-wave problem as a nonlinear elliptic boundary value problem in a fixed infinite strip, the proof uses the implicit function theorem for analytic operators. As key technical results, a priori estimates and spectral properties are derived for the linearized problem.

Original languageEnglish (US)
Pages (from-to)2550-2570
Number of pages21
JournalInternational Mathematics Research Notices
Issue number11
StatePublished - 2012

ASJC Scopus subject areas

  • General Mathematics


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