Genericity of condensation in wave kinetic equations

Determine whether condensation should be expected generically for solutions of the cubic nonlinear Schrödinger wave kinetic equation or only for particular classes of initial data and solutions.

Background

Condensation refers to the formation of a singular concentration, such as a Dirac mass at zero frequency, during the evolution of a wave kinetic equation. The paper contrasts this possibility with its perturbative result showing that sufficiently small perturbations of nonsingular Rayleigh–Jeans equilibria remain global and relax exponentially without condensation.

The cited question concerns the generality of condensation beyond the specific classes of data for which formation has been established. The paper identifies one regime where condensation does not occur but does not settle whether condensation is a generic phenomenon or restricted to particular classes of solutions.