Angeliki Menegaki (Imperial College)

Abstract: L2-stability for the 4-waves kinetic equation around the Rayleigh-Jeans equlibrium

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. In particular, introducing a cut-off on the frequencies, I will present an L2 stability of mild solutions for initial data close to Rayleigh-Jeans. If time permits, I will discuss an ongoing work on stability of radial solutions without the cut-off on the frequencies. The last part is joint work with Miguel Escobedo (UPV/EHU)."