| Abstract: |
| In this talk, we begin by introducing the explicit solution formula for the Benjamin-Ono (BO) equation obtained by Patrick Gerard. Building on this representation, we present an overview of recent numerical schemes, which provide new tools for investigating the long-time dynamics of BO.
In the setting of randomized initial data, we then explain how iterating this explicit formula, combined with non-commutative Khintchine`s inequality, yields new insights into the Wave Kinetic theory for BO, up to the physically relevant kinetic time scale.
The former results are joint work with Xi Chen (Basel), Matthieu Dolbeault (Nantes), Thierry Laurens (Wisconsin-Madison), and Ola Maehlen (Paris-Saclay), while the latter is a joint work with Gigliola Staffilani (MIT) and Felipe Hernandez (Penn State). |
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