Pierre Germain (NYU)
Derivation of the kinetic wave equation
Abstract:
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.