Joint BCAM-UPV/EHU Analysis and PDE seminar: 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, introducing a cut-off on the frequencies, I will present an $L^2$ stability of mild solutions for initial data close to Rayleigh-Jeans, when the dispersion relation is weakly perturbed around the quadratic one.

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