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Some mathematical results linked with wave turbulence theory

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If you have a question about this talk, please contact Prof. Clément Mouhot.

We consider the two-dimensional cubic Schroedinger equation posed on a large periodic box, and with small nonlinearity. We prove that under a certain regime, when the size of the box goes to infinity and the size of the nonlinearity goes to zero, the equation is driven by a continuous equation posed on the whole space, possessing very strong geometric properties. This is a joint work with Pierre Germain and Zaher Hani (NYU). Then we will discuss the connections between this equation and the kinetic Zakharov equation of wave turbulence theory. This last part is a work in progress with Laure Saint-Raymond (ENS Paris).

This talk is part of the Partial Differential Equations seminar series.

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