Peter Miller – Leverhulme Seminar

University of Michigan University of Michigan


Dispersive Shock Waves in the Benjamin-Ono Equation


Mathematical Physics Seminar


11th November 2022, 1:45 pm – 3:30 pm
Fry Building, 2.04


The Benjamin-Ono equation is a model for internal water waves in stratified fluids over an infinitely-deep lower layer. It is similar to the Korteweg-de Vries (KdV) equation, but with a different dispersive term that is nonlocal, involving the Hilbert transform. Like KdV, it has a Lax pair, although its inverse-scattering transform is not fully justified in all details to date. This talk will describe the formation of dispersive shock waves in solutions of the Benjamin-Ono equation. Weak small-dispersion limits have been established for ``quasi'' initial-value problems in the whole line setting by Miller and Xu and in the periodic setting by Gassot. After describing those results, we will explain some preliminary work on strong asymptotics to resolve the oscillations in the shock zone.





Biography:

Talk recording: https://mediasite.bris.ac.uk/Mediasite/Play/a44f705b61154de2b8cbc7bb12fed3c71d

Organiser: Emma Bailey

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