Long time justification of wave turbulence theory
arXiv:2311.10082
Abstract
In a series of previous works (arXiv:2104.11204, arXiv:2110.04565, arXiv:2301.07063), we gave a rigorous derivation of the homogeneous wave kinetic equation (WKE) up to small multiples of the kinetic timescale, which corresponds to short time solutions to the wave kinetic equation. In this work, we extend this justification to arbitrarily long times that cover the full lifespan of the WKE. This is the first large data, long-time derivation ever obtained in any nonlinear (particle or wave) collisional kinetic limit.
121 pages, 20 figures. [V2] Added the proof of Proposition 3.2 and some discussions concerning the emergence of time irreversibility