Full derivation of the wave kinetic equation

Abstract: We will discuss a recent work, in collaboration with Yu Deng (USC), in which we provide the rigorous derivation of the wave kinetic equation from the cubic nonlinear Schrödinger (NLS) equation at the kinetic timescale, under a particular scaling law that describes the limiting process. This solves a main conjecture in the theory of wave turbulence, i.e. the kinetic theory of nonlinear wave systems. Our result is the wave analog of Lanford's theorem on the derivation of the Boltzmann kinetic equation from particle systems, where in both cases one takes the thermodynamic limit as the size of the system diverges to infinity, and as the interaction strength of waves or radius of particles vanishes to 0, according to some specified scaling law. This is the first result of its kind for any nonlinear wave system.

analysis of PDEs

Audience: researchers in the topic

PDE seminar via Zoom