Title
Explicit formulas for the Benjamin–Ono equation: analysis and applications
Abstract
This talk presents recent work on the Benjamin–Ono equation, centered on the development and application of explicit formulas.
In the first part, I will present the explicit formula for the Benjamin–Ono equation on the line and explain how it can be used to study the zero dispersion limit. I will also describe how we extend this formula to square integrable and real valued initial data; this extension allows us to establish the existence of the zero dispersion limit for more singular initial data.
In the second part, I will show how the explicit formula can be used to develop a new numerical scheme for the Benjamin–Ono equation on the circle. This is my joint work with Yvonne Alama Bronsard and Matthieu Dolbeault. A key point is that we have rigorously proved the convergence of this scheme. More precisely, our error estimate has a constant that grows linearly with the final time rather than exponentially, which makes the scheme effective for long-time numerical simulations.
Please note that the seminar will take place in person in room 140 of Huxley Building.