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Small-amplitude finite-depth Stokes waves are transversally unstable

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arxiv 2409.01663 v2 pith:XCZWUAJL submitted 2024-09-03 math.AP

Ziang Jiao , L. Miguel Rodrigues , Changzhen Sun , Zhao Yang This is my paper · ORCID
classification math.AP
keywords finite-depthsmall-amplitudeunstablewavesequationsgravityinviscidirrotational
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We prove that all irrotational planar periodic traveling waves of sufficiently small-amplitude are spectrally unstable as solutions to three-dimensional inviscid finite-depth gravity water-waves equations.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Instabilities of internal gravity waves in the two-dimensional Boussinesq system

    math.AP 2025-07 conditional novelty 7.0 of 10

    Small-amplitude plane internal waves in the 2D inviscid Boussinesq system are proven to be spectrally unstable via a rigorous Floquet-Bloch analysis.

  2. On higher order isolas of unstable Stokes waves

    math.AP 2025-01 accept novelty 6.0 of 10

    For p=2,3,4, the coefficient beta_1^{(p)}(h) controlling the exponentially small width of the p-th Stokes-wave isolas has explicit deep-water asymptotics, namely (3*sqrt(3)/64)e^{-h/2}, (2*sqrt(2)/3)e^{-2h}, and -(5*s...

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