This post is based on my paper

Let us consider the acoustic wave turbulence kinetic equation

where is the collision term, describing pure resonant three-wave interactions. The equation is a three-wave kinetic one, in which the collision operator is of the form

with

We have used the short-hand notation and .

In this paper, we discover, for the first time, the connection between the wave kinetic equation and chemical reaction networks. We prove that the discrete version of the wave kinetic equation can be associated with a chemical reaction network which takes the form

As a consequence, techniques that have been used to study the Global Attractor Conjecture in chemical reaction network theory can be applied to study the long time behavior of the wave kinetic equation We prove that as time evolves, the solution of the discrete version of the wave kinetic equation converges to a steady state exponentially in time.

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