Sur les ondes de Stokes et une conjecture de Levi-Civita

Translated title of the contribution: On Stokes waves and a conjecture of Levi-Civita

Boris Buffoni, Edward Norman Dancer, John Francis Toland

Research output: Contribution to journalArticlepeer-review

11 Citations (Scopus)

Abstract

In his work [6] on Stokes waves (stationary periodic gravity waves), Levi-Civita conjectured that, for any given propagation speed c > 0, the wavelengths are not larger than 2πc2/g, where g > 0 is the acceleration due to gravity (see also [3]). We state a result on the existence of Stokes waves with arbitrarily large wavelengths, that shows no such upper-bound on the wavelength exists, and therefore that Levi-Civita's conjecture is false (see [2] for a complete proof). These long waves arise by way of sub-harmonic bifurcations. This vindicates numerical results of Saffman [9] and offers a rigorous complement to the analysis of Baesens and MacKay [1].

Translated title of the contributionOn Stokes waves and a conjecture of Levi-Civita
Original languageFrench
Pages (from-to)1265-1268
Number of pages4
JournalComptes Rendus de l'Academie des Sciences - Series I: Mathematics
Volume326
Issue number11
Publication statusPublished - Jun 1998

ASJC Scopus subject areas

  • Mathematics(all)

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