The Benjamin-Ono approximation for 2D gravity water waves with constant vorticity

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.

31 pages, 1 figure; final version

References in corpus (4)

• Steady periodic water waves with constant vorticity: regularity and local bifurcation
• Two component integrable systems modelling shallow water waves: the constant vorticity case
• Traveling quasi-periodic water waves with constant vorticity
• Nearly-Hamiltonian Structure for Water Waves with Constant Vorticity

Cited by in corpus (1)

• Two dimensional solitary water waves with constant vorticity, Part I: the deep gravity case