Home /  Graduate Student Working Group: The Benjamin-Ono approximation for low frequency gravity water waves with constant vorticity

Seminar

Graduate Student Working Group: The Benjamin-Ono approximation for low frequency gravity water waves with constant vorticity April 21, 2021 (11:10 AM PDT - 12:10 PM PDT)
Parent Program:
Location: SLMath: Online/Virtual
Speaker(s) James Rowan (University of North Carolina)
Description

To participate in this seminar, please register here: https://www.msri.org/seminars/25657

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Abstract/Media

To participate in this seminar, please register here: https://www.msri.org/seminars/25657

Abstract: It is well-known that the cubic nonlinear Schrodinger equation gives a good approximation for frequency-localized solutions to the irrotational 2D gravity water waves equations, at least on a cubic timescale.  Replacing the assumption of irrotationality with one of constant vorticity allows the model to apply to waves in settings with countercurrents, but the new terms introduced by the vorticity break the scaling symmetry, and in the low-frequency regime, they should have a large effect.  We show that, for low-frequency solutions, the Benjamin-Ono equation gives a good approximation to the 2D gravity water waves equations with constant vorticity.  The proof relies on normal form analysis and modified energy estimates.

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