5 papers · 1 filter
Global Well-Posedness near Rayleigh-Jeans Equilibria for the Cubic NLS Wave Kinetic Equation
Miguel Escobedo, Angeliki Menegaki
We study the dynamics of the kinetic wave equation associated to the three dimensional Schrödinger equation close to Rayleigh-Jeans equilibria. We first prove that the linearised o…
Local classical solutions of a kinetic equation for three waves interactions in presence of a Dirac measure at the origin
Miguel Escobedo
The existence of local, classical solutions is proved, for a system of two coupled equations that describe, in the framework of the wave turbulence theory, the fluctuations around…
Entropy maximizers for kinetic wave equations set on tori
Miguel Escobedo, Pierre Germain, Joonhyun La +1
We consider the kinetic wave equation, or phonon Boltzmann equation, set on the torus (physical system set on the lattice). We describe entropy maximizers for fixed mass and energy…
Instability of singular equilibria of a wave kinetic equation
Miguel Escobedo, Angeliki Menegaki
We consider the singular Rayleigh-Jeans equilibrium of the -waves kinetic turbulence equation for the three dimensional Schrödinger equation. We first show the formation in fini…
Regularizing effects in a linear kinetic equation for cubic interactions
Miguel Escobedo
We describe regularizing effects in the linearization of a kinetic equation that arises in study of a system of nonlinear waves satisfying the Schrödinger equation in terms of weak…