Isotropic Wave Turbulence with simplified kernels: existence, uniqueness and mean-field limit for a class of instantaneous coagulation-fragmentation processes

Abstract

The isotropic 4-wave kinetic equation is considered in its weak formulation using model (simplified) homogeneous kernels. Existence and uniqueness of solutions is proven in a particular setting where the kernels have a rate of growth at most linear. We also consider finite stochastic particle systems undergoing instantaneous coagulation- fragmentation phenomena and give conditions in which this system approximates the solution of the equation (mean-field limit).

arXiv admin note: text overlap with arXiv:math/9801145 by other authors

References in corpus (2)

• Differential equation approximations for Markov chains
• Explosion phenomena in stochastic coagulation-fragmentation models

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