Archive for Rational Mechanics and Analysis

, Volume 171, Issue 3, pp 349–416

Convexity of Stokes Waves of Extreme Form


  • P. I. Plotnikov
    • Lavryentyev Institute of HydodynamicsRussian Academy of Sciences
    • Department of Mathematical SciencesUniversity of Bath

DOI: 10.1007/s00205-003-0292-3

Cite this article as:
Plotnikov, P. & Toland, J. Arch. Rational Mech. Anal. (2004) 171: 349. doi:10.1007/s00205-003-0292-3


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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© Springer-Verlag Berlin Heidelberg 2003