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).