Seminar| Institute of Mathematical Sciences
Time: Thursday, July 9th, 2026,15:00-16:00
Location: IMS RS408
Speaker:Yao Li, University of Massachusetts Amherst
Abstract:Recent years have witnessed substantial progress in the rigorous derivation of wave kinetic equations from nonlinear Schrödinger (NLS) equations. While the Kolmogorov-Zakharov spectra -- a formal steady-state solution to the wave kinetic equation -- effectively describes energy transfer across different scales, rigorous mathematical analysis of the dynamics of energy cascade systems embedded within NLS remains notably underdeveloped. In this talk, I will outline the key challenges in analyzing energy cascade systems and present our recent progress on the existence, uniqueness, and ergodicity for a reduced energy cascade system embedded in NLS. Central to our approach is the novel Feynman-Kac-Lyapunov method we developed, which enables the construction of appropriate Lyapunov functions for the verification of the stochastic stability. These results open new pathways to understanding nonequilibrium statistical properties in wave turbulence.