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).
Highlights
Wave turbulence (Refs. 17, 18, 10, and 14, [entry turbulence]) describes weakly non-linear systems of dispersive waves
We start with a brief presentation of the general 4-wave kinetic equation[15] and move quickly to consider the isotropic case with simplified kernels, which is the object of study of the present work, and present the main results
We focus our study on the weak formulation of the isotropic 4-wave kinetic equation defined against functions in B(RN), the set of bounded measurable functions with bounded support in RN
Summary
Wave turbulence (Refs. 17, 18, 10, and 14, [entry turbulence]) describes weakly non-linear systems of dispersive waves. 17, 18, 10, and 14, [entry turbulence]) describes weakly non-linear systems of dispersive waves. The present work focuses in the case of 4 interacting waves. We start with a brief presentation of the general 4-wave kinetic equation[15] and move quickly to consider the isotropic case with simplified kernels, which is the object of study of the present work, and present the main results
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