On the Zakharov-L'vov Stochastic Model for Wave Turbulence

被引：9
|
作者：
Dymov, A., V [1 ]
Kuksin, S. B. [2 ,3 ,4 ]
机构：
[1] Russian Acad Sci, Steklov Math Inst, Moscow 119991, Russia
[2] Univ Paris Diderot Paris 7, F-75205 Paris, France
[3] Shandong Univ, Sch Math, Jinan, Peoples R China
[4] St Petersburg State Univ, St Petersburg, Russia
来源：
DOKLADY MATHEMATICS | 2020年 / 101卷 / 02期
基金：
俄罗斯科学基金会; 俄罗斯基础研究基金会;
关键词：
wave turbulence; energy spectrum; wave kinetic equation; kinetic limit; nonlinear Schrodinger equation; stochastic perturbation;
D O I：
10.1134/S1064562420020106
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
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 Schrodinger 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.
引用
收藏
页码：102 / 109
页数：8
相关论文
共 50 条
  • [21] Model of laminated wave turbulence
    Kartashova, E.
    JETP LETTERS, 2006, 83 (07) : 283 - 287
  • [22] Numerical investigation of turbulence generation using Zakharov-like model equation
    Kumar, Praveen
    Uma, R.
    Sharma, R. P.
    PHYSICS OF FLUIDS, 2024, 36 (04)
  • [23] Role of dissipation in flexural wave turbulence: From experimental spectrum to Kolmogorov-Zakharov spectrum
    Miquel, Benjamin
    Alexakis, Alexandros
    Mordant, Nicolas
    PHYSICAL REVIEW E, 2014, 89 (06)
  • [24] Random Wave Equation for the Stochastic Quantum Zakharov-Kuznetsov Equation and Their Exact Solutions
    Mohammed, Wael W.
    Sidaoui, Rabeb
    Alshammari, Hessa W.
    Algolam, Mohamed S.
    EUROPEAN JOURNAL OF PURE AND APPLIED MATHEMATICS, 2025, 18 (01):
  • [25] Turbulence generation from a stochastic wavelet model
    Du, Y.
    Lin, G.
    PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, 2018, 474 (2217):
  • [26] Pickup ion turbulence: A Stochastic growth model
    Zank, GP
    Cairns, IH
    OUTER HELIOSPHERE: THE NEXT FRONTIERS, PROCEEDINGS, 2001, 11 : 125 - 128
  • [27] BURGERS MODEL OF TURBULENCE AS A STOCHASTIC-PROCESS
    BREUER, HP
    PETRUCCIONE, F
    JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 1992, 25 (11): : L661 - L667
  • [28] Large deviations for the stochastic shell model of turbulence
    Manna, U.
    Sritharan, S. S.
    Sundar, P.
    NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS, 2009, 16 (04): : 493 - 521
  • [29] Large deviations for the stochastic shell model of turbulence
    U. Manna
    S. S. Sritharan
    P. Sundar
    Nonlinear Differential Equations and Applications NoDEA, 2009, 16 : 493 - 521
  • [30] A Lagrangian stochastic model for dispersion in stratified turbulence
    Das, SK
    Durbin, PA
    PHYSICS OF FLUIDS, 2005, 17 (02) : 1 - 10
12345