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Convexity of Stokes Waves of Extreme Form

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Abstract

Existence is established of a piecewise-convex, periodic, planar curve S below which is defined a harmonic function which simultaneously satisfies prescribed Dirichlet and Neumann boundary conditions on S. In hydrodynamics this corresponds to the existence of a periodic Stokes wave of extreme form which has a convex profile between consecutive stagnation points where there is a corner with a contained angle of 120°

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Authors and Affiliations

  1. Lavryentyev Institute of Hydodynamics, Russian Academy of Sciences, Lavryentyev pr. 15, Novosibirsk, 630090, Russia

    P. I. Plotnikov

  2. Department of Mathematical Sciences, University of Bath, Claverton Down, Bath BA2 7AY, United Kingdom

    J. F. Toland

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  1. P. I. Plotnikov
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  2. J. F. Toland
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Correspondence to J. F. Toland.

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Plotnikov, P., Toland, J. Convexity of Stokes Waves of Extreme Form. Arch. Rational Mech. Anal. 171, 349–416 (2004). https://doi.org/10.1007/s00205-003-0292-3

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