Derivation of the Wave Kinetic Equation: Full Range of Scaling Laws

Yu Deng, University of Chicago, Illinois. Zaher Hani, University of Michigan, Ann Arbor, Michigan

Chapters; 1. Introduction; 2. Preparations; 3. Overview of the proof; 4. Couples and molecules; 5. Vines and twists; 6. $\mathcal {K}_\mathcal {Q}$ estimates for regular couples and regular trees; 7. $\mathcal {K}_\mathcal {Q}$ estimates for vines; 8. Reduction to counting estimates; 9. Reduction to large gap molecules; 10. Counting problem for large gap molecules; 11. Linearization and the end of the proof; A. Auxiliary results; B. The algorithm for large gap molecules