On invariant Gibbs measures conditioned on mass and momentum

DOI10.2969/jmsj/06510013zbMath1274.60214arXiv1012.3432OpenAlexW2962886842MaRDI QIDQ1946848

Tadahiro Oh, Jeremy Quastel

Publication date: 9 April 2013

Published in: Journal of the Mathematical Society of Japan (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1012.3432

zbMATH Keywords

Schrödinger equationGibbs measureLévy areaKortweg-de Vries equation

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) Applications of stochastic analysis (to PDEs, etc.) (60H30) White noise theory (60H40) NLS equations (nonlinear Schrödinger equations) (35Q55)

Related Items (9)

Hydrodynamic equations for the Ablowitz–Ladik discretization of the nonlinear Schrödinger equation ⋮ Gibbs measure for the higher order modified Camassa-Holm equation ⋮ Invariant Measures and the Soliton Resolution Conjecture ⋮ Gibbs measures of nonlinear Schrödinger equations as limits of many-body quantum states in dimensions \({d \leqslant 3}\) ⋮ Invariant measure construction at a fixed mass ⋮ Derivation of nonlinear Gibbs measures from many-body quantum mechanics ⋮ Invariance of white noise for KdV on the line ⋮ Gibbs Measures of Nonlinear Schrödinger Equations as Limits of Quantum Many-Body States in Dimension d ≤ 3 ⋮ Optimal integrability threshold for Gibbs measures associated with focusing NLS on the torus

Cites Work

• Invariance of the Gibbs measure for the periodic quartic gKdV
• Interpolation of Gibbs measures with white noise for Hamiltonian PDE
• Ergodic behavior of diagonal measures and a theorem of Szemeredi on arithmetic progressions
• Fourier transform restriction phenomena for certain lattice subsets and applications to nonlinear evolution equations. I: Schrödinger equations
• Periodic nonlinear Schrödinger equation and invariant measures
• Statistical mechanics of the nonlinear Schrödinger equation.
• A remark on normal forms and the ``I-method for periodic NLS
• System Control and Rough Paths
• Le Mouvement Brownien Plan
• Korteweg-de Vries and nonlinear Schrödinger equations: qualitative theory
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