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)."