## 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 2πc^{2}/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 contribution | On Stokes waves and a conjecture of Levi-Civita |
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Original language | French |

Pages (from-to) | 1265-1268 |

Number of pages | 4 |

Journal | Comptes Rendus de l'Academie des Sciences - Series I: Mathematics |

Volume | 326 |

Issue number | 11 |

Publication status | Published - Jun 1998 |

## ASJC Scopus subject areas

- General Mathematics