In his work  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 ). 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  for a complete proof). These long waves arise by way of sub-harmonic bifurcations. This vindicates numerical results of Saffman  and offers a rigorous complement to the analysis of Baesens and MacKay .
|Translated title of the contribution||On Stokes waves and a conjecture of Levi-Civita|
|Number of pages||4|
|Journal||Comptes Rendus de l'Academie des Sciences - Series I: Mathematics|
|Publication status||Published - Jun 1998|
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