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Doklady Rossijskoj Akademii Nauk. Mathematika, Informatika, Processy Upravlenia, 2020, Volume 491, Pages 29–37
DOI: https://doi.org/10.31857/S2686954320020101 (Mi danma4) 		 
This article is cited in 5 scientific papers (total in 5 papers)

MATHEMATICS

On the Zakharov–Lvov stochastic model for wave turbulence

A. V. Dymova, S. B. Kuksinbcd

a Steklov Mathematical Institute of Russian Academy of Sciences, Moscow
b Université Paris VII – Denis Diderot
c Shandong University, Jinan, PRC
d Saint Petersburg State University
Full-text PDF (438 kB) Citations (5)
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DOI: https://doi.org/10.31857/S2686954320020101
Abstract: 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.
Funding agency Grant number
Russian Foundation for Basic Research 18-31-20031
Russian Science Foundation 18-11-00032
A. Dymov was supported by the Russian Foundation for Basic Research according to the research project 18-31-20031, and S. Kuksin, by the grant 18-11-00032 of Russian Science Foundation.
Presented: D. V. Treschev
Received: 09.11.2019
Revised: 09.11.2019
Accepted: 21.01.2020
English version:
Doklady Mathematics, 2020, Volume 101, Issue 2, Pages 102–109
DOI: https://doi.org/10.1134/S1064562420020106
Bibliographic databases:
Document Type: Article
UDC: 517.938, 517.958, 51-73
Language: Russian
Citation: A. V. Dymov, S. B. Kuksin, “On the Zakharov–Lvov stochastic model for wave turbulence”, Dokl. RAN. Math. Inf. Proc. Upr., 491 (2020), 29–37; Dokl. Math., 101:2 (2020), 102–109
Citation in format AMSBIB
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