Variational Instability for Irrotational Water Waves in Finite Depth

Florian Kogelbauer

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arXiv · 2502.16698

Variational Instability for Irrotational Water Waves in Finite Depth

Florian Kogelbauer

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Abstract

We prove variational instability for small-amplitude solutions to the periodic irrotational gravity water wave problem in finite depth. Our results are based on a reformation of the water wave problem as a pseudo-differential Euler-Lagrange equation together with the local existence theory of small-amplitude waves. We use a perturbative spectral analysis of the second-variation operator in combination with a Plotnikov transformation to show instability for non-trivial solutions.

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Florian Kogelbauer. 2025-02-23. Variational Instability for Irrotational Water Waves in Finite Depth. https://arxiv.org/abs/2502.16698

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