English

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.

Keywords

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

R2 v1 2026-06-24T05:16:17.235Z