Title: Wave turbulence for the Nonlinear Schrodinger equation
Speaker: Prof. Jalal Shatah (美国科学与艺术院士) (Courant Institute of New York University)
Time: 2018-7-6, 16:20-17:20
Place: N820
Abstract: Wave turbulence describes the out-of-equilibrium statistical mechanics of weakly nonlinear waves. It was first put forward by Peierls in 1928, in the context of solid state physics, and then by Hasselman in 1962, in the context of water waves. The theory was invigorated and investigated by Zakharov and his school in the 70’s. The theory of weak turbulence proposed by Zakharov relies on the derivation of a kinetic wave equation. In this talk we will derive the kinetic equation for the nonlinear Schr\"odinger equation and discuss the time scale where the kinetic equation is a valid approximation.