Analytical study of a generalized Dirichlet-Neumann operator for three-dimensional water waves with vorticity
Abstract
In this paper we consider three-dimensional water waves with vorticity, under the action of gravity. We discuss a generalized Zakharov-Craig-Sulem formulation of the problem introduced by Castro and Lannes, which involves a generalized Dirichlet-Neumann operator. We study this operator in detail, extending some well-known results about the classical Dirichlet-Neumann operator for irrotational water waves, such as the Taylor expansion in homogeneous powers of the wave profile, the computation of its differential and a paralinearization result. We stress the fact that no geometric condition on either the velocity field or the vorticity is assumed.
Keywords
Cite
@article{arxiv.2502.09370,
title = {Analytical study of a generalized Dirichlet-Neumann operator for three-dimensional water waves with vorticity},
author = {S. Pasquali},
journal= {arXiv preprint arXiv:2502.09370},
year = {2025}
}
Comments
changes with respect to previous version: proofs in Secc.4-7 and in Appendix A rewritten in a more concise way, some typos corrected, references updated