Gibbs measure evolution in radial nonlinear wave and Schrödinger equations on the ball

DOI10.1016/j.crma.2012.05.006zbMath1251.35141arXiv1205.1187OpenAlexW2007102559MaRDI QIDQ447880

Jean Bourgain, Aynur Bulut

Publication date: 30 August 2012

Published in: Comptes Rendus. Mathématique. Académie des Sciences, Paris (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1205.1187

Mathematics Subject Classification ID

Second-order nonlinear hyperbolic equations (35L70) NLS equations (nonlinear Schrödinger equations) (35Q55) PDEs with randomness, stochastic partial differential equations (35R60) PDEs with measure (35R06)

Related Items (8)

Gibbs measures of nonlinear Schrödinger equations as limits of many-body quantum states in dimensions \({d \leqslant 3}\) ⋮ Invariant Gibbs measure evolution for the radial nonlinear wave equation on the 3d ball ⋮ Almost sure global well posedness for the radial nonlinear Schrödinger equation on the unit ball I: the 2D case ⋮ Randomization and the Gross-Pitaevskii hierarchy ⋮ Almost sure well-posedness for the periodic 3D quintic nonlinear Schrödinger equation below the energy space ⋮ Local existence of solutions to randomized Gross-Pitaevskii hierarchies ⋮ Almost sure global well-posedness for the radial nonlinear Schrödinger equation on the unit ball. II: the 3D case ⋮ Gibbs Measures of Nonlinear Schrödinger Equations as Limits of Quantum Many-Body States in Dimension d ≤ 3

Cites Work

• Random data Cauchy theory for supercritical wave equations I: Local theory
• Invariant measures for the defocusing nonlinear Schrödinger equation
• Fourier transform restriction phenomena for certain lattice subsets and applications to nonlinear evolution equations. I: Schrödinger equations
• Fourier transform restriction phenomena for certain lattice subsets and applications to nonlinear evolution equations. II: The KdV-equation
• Periodic nonlinear Schrödinger equation and invariant measures
• Invariant measures for the Gross-Pitaevskii equation
• Invariant measures for the 2D-defocusing nonlinear Schrödinger equation
• Invariant measures for the nonlinear Schrödinger equation on the disc
• A remark on normal forms and the ``I-method for periodic NLS
• The Cauchy problem for nonlinear Schrödinger equation (NLS) with critical nonlinearity

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