Onset of the wave turbulence description of the longtime behavior of the nonlinear Schrödinger equation
DOI10.1007/s00222-021-01039-zzbMath1484.35345arXiv1907.03667OpenAlexW3139261203MaRDI QIDQ2049904
Pierre Germain, Jalal Shatah, Zaher Hani, Tristan Buckmaster
Publication date: 27 August 2021
Published in: Inventiones Mathematicae (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1907.03667
Asymptotic behavior of solutions to PDEs (35B40) A priori estimates in context of PDEs (35B45) NLS equations (nonlinear Schrödinger equations) (35Q55) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02) Boltzmann equations (35Q20)
Related Items (19)
Cites Work
- Unnamed Item
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- From Newton to Boltzmann: hard spheres and short-range potentials
- The energy-critical defocusing NLS on \({\mathbb{T}}^{3}\)
- On the continuous resonant equation for NLS. II: Statistical study
- Weakly nonlinear Schrödinger equation with random initial data
- A one-dimensional model for dispersive wave turbulence
- Wave turbulence.
- The phonon Boltzmann equation, properties and link to weakly anharmonic lattice dynamics
- Some considerations on the derivation of the nonlinear quantum Boltzmann equation. II: The low density regime
- On the continuous resonant equation for NLS. I: Deterministic analysis.
- Random data Cauchy theory for supercritical wave equations I: Local theory
- Quantum diffusion of the random Schrödinger evolution in the scaling limit
- Not to normal order-notes on the kinetic limit for weakly interacting quantum fluids
- Fourier transform restriction phenomena for certain lattice subsets and applications to nonlinear evolution equations. I: Schrödinger equations
- Optimal local well-posedness theory for the kinetic wave equation
- On the energy cascade of 3-wave kinetic equations: beyond Kolmogorov-Zakharov solutions
- Linearized wave turbulence convergence results for three-wave systems
- On the quantum Boltzmann equation
- Some considerations on the derivation of the nonlinear quantum Boltzmann equation
- Strichartz estimates for the Schrödinger equation on irrational tori
- On the propagation of weakly nonlinear random dispersive waves
- Quantum diffusion of the random Schrödinger evolution in the scaling limit. II: The recollision diagrams
- From the \(N\)-body Schrödinger equation to the quantum Boltzmann equation: a term-by-term convergence result in the weak coupling regime
- On the theory of Weak Turbulence for the Nonlinear Schrödinger Equation
- Wave Turbulence: A Story Far from Over
- On the non-linear energy transfer in a gravity-wave spectrum Part 1. General theory
- Time evolution of large classical systems
- The Fourth Power Moment of the Riemann Zeta Function
- Effective Dynamics of the Nonlinear Schrödinger Equation on Large Domains
- Lecture Notes on Quantum Brownian Motion
- On the non-linear energy transfer in a gravity wave spectrum Part 2. Conservation theorems; wave-particle analogy; irrevesibility
- The weakly nonlinear large-box limit of the 2D cubic nonlinear Schrödinger equation
- Derivation of the transport equation for electrons moving through random impurities
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