Global dynamics for the stochastic KdV equation with white noise as initial data
DOI10.1090/btran/178arXiv2308.04576OpenAlexW4392014775MaRDI QIDQ6191377
Jeremy Quastel, Philippe Sosoe, Tadahiro Oh
Publication date: 7 March 2024
Published in: Transactions of the American Mathematical Society, Series B (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2308.04576
invariant measurewhite noiseKorteweg-de Vries equationstochastic Korteweg-de Vries equationevolution system of measures
KdV equations (Korteweg-de Vries equations) (35Q53) Applications of stochastic analysis (to PDEs, etc.) (60H30) White noise theory (60H40) Existence problems for PDEs: global existence, local existence, non-existence (35A01) PDEs with randomness, stochastic partial differential equations (35R60) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02) PDEs with measure (35R06)
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- 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
- Modulation spaces, Wiener amalgam spaces, and Brownian motions
- Global wellposedness of KdV in \(H^{-1}(\mathbb T,\mathbb R)\)
- Symplectic nonsqueezing of the Korteweg-de Vries flow
- 2D stochastic Navier-Stokes equations with a time-periodic forcing term
- Periodic stochastic Korteweg-de Vries equation with additive space-time white noise
- KdV preserves white noise
- Invariance of the white noise for KdV
- Gaussian measures in Banach spaces
- Fourier transform restriction phenomena for certain lattice subsets and applications to nonlinear evolution equations. II: The KdV-equation
- On the stochastic Korteweg-de Vries equation
- The stochastic Korteweg-de Vries equation in \(L^2(\mathbb{R})\)
- Periodic nonlinear Schrödinger equation and invariant measures
- Periodic Korteweg-de Vries equation with measures as initial data
- Discretisations of rough stochastic PDEs
- Quasi-invariant Gaussian measures for the cubic fourth order nonlinear Schrödinger equation
- White noise driven Korteweg-de Vries equation
- Global well-posedness of the one-dimensional cubic nonlinear Schrödinger equation in almost critical spaces
- Invariance of white noise for KdV on the line
- Almost conservation laws for stochastic nonlinear Schrödinger equations
- Normal form approach to the one-dimensional periodic cubic nonlinear Schrödinger equation in almost critical Fourier-Lebesgue spaces
- On the parabolic and hyperbolic Liouville equations
- KdV is well-posed in \(H^{-1}\)
- Low regularity conservation laws for integrable PDE
- Transformations of Wiener integrals under translations
- Multilinear weighted convolution of L 2 functions, and applications to nonlinear dispersive equations
- On the probabilistic Cauchy theory of the cubic nonlinear Schrödinger equation on ℝ^{𝕕}, 𝕕≥3
- On the Cameron–Martin theorem and almost-sure global existence
- Partial Differential Equations for Probabilists
- White noise for KdV and mKdV on the circle
- Mouvement brownien et espaces de besov
- STOCHASTIC NONLINEAR SCHRÖDINGER EQUATION WITH ALMOST SPACE–TIME WHITE NOISE
- Analysis in Banach Spaces
- Non-Existence of Solutions for the Periodic Cubic NLS below ${L}^{{2}}$
- Periodic Solutions of the Korteweg--de Vries Equation Driven by White Noise
- Sharp global well-posedness for KdV and modified KdV on ℝ and 𝕋
- Stochastic integration of functions with values in a Banach space
- A bilinear estimate with applications to the KdV equation
- Random Data Wave Equations
- Global Dynamics for the Two-dimensional Stochastic Nonlinear Wave Equations
- Solving the 4NLS with white noise initial data
- On the Probabilistic Cauchy Theory for Nonlinear Dispersive PDEs
- Introduction to Stochastic Analysis and Malliavin Calculus
- Probabilistic global well-posedness of the energy-critical defocusing quintic nonlinear wave equation on \(\mathbb R^3\)
- Stochastic nonlinear wave dynamics on compact surfaces
This page was built for publication: Global dynamics for the stochastic KdV equation with white noise as initial data
