The Benjamin-Ono approximation for low frequency gravity water waves with constant vorticity

The HADES seminar on Tuesday, September 21st, will be given by James Rowan from at 5 pm in 740 Evans.

Speaker: James Rowan (University of California, Berkeley)

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.  This work is joint with Mihaela Ifrim, Daniel Tataru, and Lizhe Wan.  Along the way to this result, I will give a brief introduction to some topics in nonlinear dispersive PDE and fluid dynamics.

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