The large-period limit for equations of discrete turbulence

DOI10.1007/s00023-023-01366-2zbMath1529.35464arXiv2104.11967OpenAlexW4312109067MaRDI QIDQ6054116

A. V. Dymov, Sergej B. Kuksin, S. G. Vleduts, Alberto Mario Maiocchi

Publication date: 24 October 2023

Published in: Annales Henri Poincaré (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2104.11967

zbMATH Keywords

asymptotic behaviornonlinear Schrödinger equationenergy spectrumquasi-solutionFeynman diagramDuhamel's formulawave kinetic equationdamped/driven problemHeath-Brown methodZakharov-L'vov setting

Mathematics Subject Classification ID

Gaussian processes (60G15) Stochastic analysis applied to problems in fluid mechanics (76M35) NLS equations (nonlinear Schrödinger equations) (35Q55) PDEs with randomness, stochastic partial differential equations (35R60) Fundamentals of turbulence (76F02) Time-dependent Schrödinger equations and Dirac equations (35Q41)

Related Items (2)

A refinement of Heath-Brown's theorem on quadratic forms ⋮ Asymptotic expansions for a class of singular integrals emerging in non-linear wave systems

Cites Work

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• Weakly nonlinear Schrödinger equation with random initial data
• Wave turbulence.
• Derivation of the cubic nonlinear Schrödinger equation from quantum dynamics of many-body systems
• Onset of the wave turbulence description of the longtime behavior of the nonlinear Schrödinger equation
• Ergodicity, mixing and KAM
• Formal expansions in stochastic model for wave turbulence. II: Method of diagram decomposition
• Linearized wave turbulence convergence results for three-wave systems
• On the Zakharov-L'vov stochastic model for wave turbulence
• On the number of points of algebraic sets over finite fields
• Derivation of a wave kinetic equation from the resonant-averaged stochastic NLS equation
• Ergodicity for a class of Markov processes and applications to randomly forced PDE's. II
• Formal expansions in stochastic model for wave turbulence. I: Kinetic limit
• Time-Averaging for Weakly Nonlinear CGL Equations with Arbitrary Potentials
• A new form of the circle method, and its application to quadratic forms.
• Gaussian Hilbert Spaces
• Linear Boltzmann equation as the weak coupling limit of a random Schrödinger equation
• Effective Dynamics of the Nonlinear Schrödinger Equation on Large Domains
• On the derivation of the wave kinetic equation for NLS
• Wave Turbulence
• The weakly nonlinear large-box limit of the 2D cubic nonlinear Schrödinger equation
• Full derivation of the wave kinetic equation

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