Random tensors, propagation of randomness, and nonlinear dispersive equations

DOI10.1007/s00222-021-01084-8zbMath1506.35208arXiv2006.09285OpenAlexW3212208789MaRDI QIDQ2131227

Andrea R. Nahmod, Haitian Yue, Yu Deng

Publication date: 25 April 2022

Published in: Inventiones Mathematicae (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2006.09285

zbMATH Keywords

nonlinear Schrödinger equationspropagating randomness

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) A priori estimates in context of PDEs (35B45) NLS equations (nonlinear Schrödinger equations) (35Q55) Constructive quantum field theory (81T08) Stochastic partial differential equations (aspects of stochastic analysis) (60H15) Existence problems for PDEs: global existence, local existence, non-existence (35A01) PDEs with randomness, stochastic partial differential equations (35R60) Time-dependent Schrödinger equations and Dirac equations (35Q41) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02) Strong solutions to PDEs (35D35) Matrix models and tensor models for quantum field theory (81T32)

Related Items (14)

Probabilistic local Cauchy theory of the cubic nonlinear wave equation in negative Sobolev spaces ⋮ A microscopic derivation of Gibbs measures for the 1D focusing cubic nonlinear Schrödinger equation ⋮ Large deviations principle for the cubic NLS equation ⋮ On the probabilistic well-posedness of the two-dimensional periodic nonlinear Schrödinger equation with the quadratic nonlinearity \(|u|^2\) ⋮ Deterministic dynamics and randomness in PDE. Abstracts from the workshop held May 22--28, 2022 ⋮ Almost sure global well-posedness for the fourth-order nonlinear Schrödinger equation with large initial data ⋮ The wave maps equation and Brownian paths ⋮ Invariant Gibbs dynamics for the two-dimensional Zakharov-Yukawa system ⋮ Probabilistic small data global well-posedness of the energy-critical Maxwell-Klein-Gordon equation ⋮ Stochastic nonlinear Schrödinger equations in the defocusing mass and energy critical cases ⋮ Three-dimensional stochastic cubic nonlinear wave equation with almost space-time white noise ⋮ Universality results for a class of nonlinear wave equations and their Gibbs measures ⋮ Invariant Gibbs measure and global strong solutions for the Hartree NLS equation in dimension three ⋮ On scattering asymptotics for the 2D cubic resonant system

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