May 23 – 24, 2024
École polytechnique
Europe/Paris timezone

Scattering, random phase and wave turbulence

May 24, 2024, 11:15 AM
Amphi Curie (École polytechnique)

Amphi Curie

École polytechnique

Route de Saclay, 91120 Palaiseau


Antoine Mouzard


The theory of wave turbulence aims at a description of the nonlinear interaction of a large number of waves. In this talk, I will present a family of initial data for the cubic two-dimensional nonlinear Schrödinger equation on the real plane, motivated by the link between regularity of the resonant manifold and dispersive properties of the equation and scattering phenomena. These initial data are periodic functions embedded in the whole space by Gaussian truncation and we are able to describe the time evolution in various time scales for deterministic and random initial data, in the limit of a large number of periods and small initial data. This allows explicit computations and we identify two different regimes where the time evolution converges towards the kinetic operator but with different forms of convergence, coming from resonances or quasiresonances. This is a joint work with Erwan Faou.

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