English

Long time justification of wave turbulence theory

Analysis of PDEs 2024-04-09 v2 Mathematical Physics math.MP

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.

Keywords

Cite

@article{arxiv.2311.10082,
  title  = {Long time justification of wave turbulence theory},
  author = {Yu Deng and Zaher Hani},
  journal= {arXiv preprint arXiv:2311.10082},
  year   = {2024}
}

Comments

121 pages, 20 figures. [V2] Added the proof of Proposition 3.2 and some discussions concerning the emergence of time irreversibility