Pierre Germain (NYU)

Derivation of the kinetic wave equation

It is conjectured by physicists that, in the proper scaling, turbulent behavior in nonlinear dispersive equations can be modeled by kinetic models, similar to Boltzmann's equation arising from Newtonian dynamics. I will present results obtained with Charles Collot, which prove this conjecture up to the kinetic time scale less an arbitrarily small power. The proof relies on the analysis of Feynman graphs in the framework of Bourgain spaces.