Variational Instability for Irrotational Water Waves in Finite Depth
Analysis of PDEs
2025-02-25 v1
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.
Cite
@article{arxiv.2502.16698,
title = {Variational Instability for Irrotational Water Waves in Finite Depth},
author = {Florian Kogelbauer},
journal= {arXiv preprint arXiv:2502.16698},
year = {2025}
}