Invariance of the white noise for KdV

DOI10.1007/s00220-009-0856-7zbMath1185.35237arXiv0904.2818OpenAlexW2060405181MaRDI QIDQ1048131

Tadahiro Oh

Publication date: 11 January 2010

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0904.2818

zbMATH Keywords

white noiseKorteweg-de Vries equationabstract Wiener spacesBourgain spaces

Mathematics Subject Classification ID

Gaussian processes (60G15) Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) KdV equations (Korteweg-de Vries equations) (35Q53) PDEs with randomness, stochastic partial differential equations (35R60) Stochastic methods applied to problems in equilibrium statistical mechanics (82B31) Probability theory on linear topological spaces (60B11)

Related Items (22)

Gibbs measure for the higher order modified Camassa-Holm equation ⋮ Invariance of the Gibbs measures for periodic generalized Korteweg-de Vries equations ⋮ QUASIINVARIANT GAUSSIAN MEASURES FOR ONE-DIMENSIONAL HAMILTONIAN PARTIAL DIFFERENTIAL EQUATIONS ⋮ Invariant Measures and the Soliton Resolution Conjecture ⋮ Random Data Cauchy Theory for Nonlinear Wave Equations of Power-Type on ℝ³ ⋮ Quasi-invariant Gaussian measures for the cubic fourth order nonlinear Schrödinger equation ⋮ Almost sure well-posedness of the cubic nonlinear Schrödinger equation below \(L^{2}(\mathbb{T})\) ⋮ Interpolation of Gibbs measures with white noise for Hamiltonian PDE ⋮ Global dynamics for the stochastic KdV equation with white noise as initial data ⋮ New non degenerate invariant measures for the Benjamin-Ono equation ⋮ Hydrodynamic models ⋮ Modulation spaces, Wiener amalgam spaces, and Brownian motions ⋮ Weak vorticity formulation of 2D Euler equations with white noise initial condition ⋮ Solving the 4NLS with white noise initial data ⋮ Randomization and the Gross-Pitaevskii hierarchy ⋮ Invariant measures and long time behaviour for the Benjamin-Ono equation. III ⋮ On the transport of Gaussian measures under the flow of Hamiltonian PDEs ⋮ Invariance of white noise for KdV on the line ⋮ Local existence of solutions to randomized Gross-Pitaevskii hierarchies ⋮ Invariance of the white noise for the Ostrovsky equation ⋮ On the Cameron–Martin theorem and almost-sure global existence ⋮ Periodic stochastic high-order Degasperis–Procesi equation with cylindrical fBm

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