Seminario di Analisi Matematica

Il 24/6/2026 alle ore 15:00, Fabio Pusateri (Università di Toronto) terrà un Seminario di Analisi Matematica dal titolo "Water Waves: Random solutions and kinetic equations in Wave Turbulence".

Abstract: We present some recent result on the construction of long-time random solutions for the full water waves equations.
We consider the pure gravity water waves system in two dimensions set on a large torus of size R; for randomly distributed initial data of small amplitude $\varepsilon$ (hence of large energy $\sim \varepsilon R^{1/2}$) we construct long lived solutions on a time scale $T \sim \varespilon^{-8/3}$. This is the first result on the construction of random solutions for quasilinear/fluids equations. 
This work is motivated by the outstanding open problem of rigorously justifying the Wave Turbulence (WT) theory set forth by Hasselman in the 60s and developed by Zakharov and others since then. 
If time permits we will also discuss ongoing work on the well-posedness of the kinetic equations associated with the water waves systems that are formally predicted by the WT theory.

This talk is based on joint works with Yu Deng (U Chicago) and Alex Ionescu (Princeton).


Il seminario si svolgerà in presenza presso il Dipartimento di Matematica e Fisica, Lungotevere Dante 376, aula M1.