Equivalent formulations for steady periodic water waves of fixed mean-depth with discontinuous vorticity
Analysis of PDEs
2024-09-16 v1
Abstract
In this work we prove the equivalence between three different weak formulations of the steady periodic water wave problem where the vorticity is discontinuous. In particular, we prove that generalised versions of the standard Euler and stream function formulation of the governing equations are equivalent to a weak version of the recently introduced modified-height formulation. The weak solutions of these formulations are considered in H\"older spaces.
Keywords
Cite
@article{arxiv.2409.08720,
title = {Equivalent formulations for steady periodic water waves of fixed mean-depth with discontinuous vorticity},
author = {Silvia Sastre-Gómez},
journal= {arXiv preprint arXiv:2409.08720},
year = {2024}
}