## Mathematical Physics and Harmonic Analysis Seminar

**Date: ** November 10, 2023

**Time: ** 1:50PM - 2:50PM

**Location: ** Zoom

**Speaker: **Angeliki Menegaki, IHES

**Title: ***L^2-stability for the 4-waves kinetic equation around the Rayleigh-Jeans equilibrium*

**Abstract: **We consider the four-waves spatial homogeneous kinetic equation arising in weak wave turbulence theory. In this talk I will present some new results on the existence and long-time behaviour of solutions around the Rayleigh-Jeans thermodynamic equilibrium solutions. In particular, I will present an $L^2$ stability of mild solutions on the whole frequency space for initial data close to Rayleigh-Jeans when assuming radial solutions for the equation, as well as a stability of the same kind without the radial solution-assumption but after introducing a cut-off on the frequencies. Parts of this talk are joint works with Miguel Escobedo (UPV/EHU).