[GS_M_APP] The rigorous derivation of the wave kinetic equation for NLS and Klein-Gordon equation
ABSTRACT
The wave kinetic equation is expected to describe the long-time statistical behavior of weakly nonlinear dispersive waves and serves as a fundamental object in wave turbulence theory. In this talk, I will present an overview of the recent rigorous derivation of the wave kinetic equation for nonlinear Schrödinger equations due to Yu Deng and Zaher Hani (`19-`23). I will first introduce the basic kinetic picture and explain how diagrammatic expansions and resonance relations arise in the analysis. I will then discuss the molecule formalism, which provides an efficient framework for organizing the combinatorial structures appearing in the proof. Finally, I will briefly report on ongoing joint work concerning the derivation of the wave kinetic equation for the Klein–Gordon equation motivated by models of anharmonic crystals. This is joint work with Zaher Hani (University of Michigan) and Katja Vassilev (University of Chicago). This talk substantially overlaps with my talk given on June 24.
