Geodesic
On the Zakharov--Lvov stochastic model for wave turbulence
Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ, Tome 491 (2020), pp. 29-37

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In this paper we discuss a number of rigorous results in the stochastic model for wave turbulence due to Zakharov–L'vov. Namely, we consider the damped/driven (modified) cubic nonlinear Schrödinger equation on a large torus and decompose its solutions to formal series in the amplitude. We show that when the amplitude goes to zero and the torus’ size goes to infinity the energy spectrum of the quadratic truncation of this series converges to a solution of the damped/driven wave kinetic equation. Next we discuss higher order truncations of the series.
Keywords: wave turbulence, energy spectrum, wave kinetic equation, kinetic limit, nonlinear Schrödinger equation, stochastic perturbation. 
@article{DANMA_2020_491_a5,
     author = {A. V. Dymov and S. B. Kuksin},
     title = {On the {Zakharov--Lvov} stochastic model for wave turbulence},
     journal = {Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleni\^a},
     pages = {29--37},
     publisher = {mathdoc},
     volume = {491},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DANMA_2020_491_a5/}
}
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A. V. Dymov; S. B. Kuksin. On the Zakharov--Lvov stochastic model for wave turbulence. Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ, Tome 491 (2020), pp. 29-37. http://geodesic.mathdoc.fr/item/DANMA_2020_491_a5/