The Benjamin-Ono approximation for 2D gravity water waves with constant vorticity
Analysis of PDEs
2022-07-19 v3
Abstract
This article is concerned with infinite depth gravity water waves with constant vorticity in two space dimensions. We consider this system expressed in position-velocity potential holomorphic coordinates. We show that, for low-frequency solutions, the Benjamin-Ono equation gives a good and stable approximation to the system on the natural cubic time scale. The proof relies on refined cubic energy estimates and perturbative analysis.
Cite
@article{arxiv.2108.08964,
title = {The Benjamin-Ono approximation for 2D gravity water waves with constant vorticity},
author = {Mihaela Ifrim and James Rowan and Daniel Tataru and Lizhe Wan},
journal= {arXiv preprint arXiv:2108.08964},
year = {2022}
}
Comments
31 pages, 1 figure; final version