Stable and unstable Stokes waves
Massimiliano Berti1
1 SISSA, Via Bonomea 265, 34136 Trieste, Italy
Séminaire Laurent Schwartz — EDP et applications (2023-2024), Talk no. 19, 14 p.

In the last years much progress has been achieved concerning the problem of determining the stability/instability of Stokes waves, i.e. periodic traveling solutions of the pure gravity water waves equations in an ocean of depth h>0, subject to longitudinal perturbations. In this talk we review some of these results focusing the attention on the existence of unstable spectral bands away from zero for Stokes waves of small amplitude ε>0. In [11] we prove that the unstable spectrum is the union of “isolas” of approximately elliptical shape, parameterized by integers p≥2, with semiaxis of size |β 1 (p) (h)|ε p +O(ε p+1 ) where β 1 (p) (h) is a nonzero analytic function of the depth h that depends on the Taylor coefficients of the Stokes waves up to order p.

Published online:
DOI: 10.5802/slsedp.166
Massimiliano Berti 1

1 SISSA, Via Bonomea 265, 34136 Trieste, Italy 
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Massimiliano Berti. Stable and unstable Stokes waves. Séminaire Laurent Schwartz — EDP et applications (2023-2024), Talk no. 19, 14 p. doi : 10.5802/slsedp.166. https://proceedings.centre-mersenne.org/articles/10.5802/slsedp.166/

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