On the Cameron–Martin theorem and almost-sure global existence
From MaRDI portal
Publication:2806130
DOI10.1017/S0013091515000218zbMath1347.60087arXiv1405.7323OpenAlexW2963138355MaRDI QIDQ2806130
Publication date: 13 May 2016
Published in: Proceedings of the Edinburgh Mathematical Society (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1405.7323
white noiseGibbs measureCameron-Martin theoremalmost-sure global existencenonlinear Hamiltonian partial differential equationrough random perturbation
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
On the probabilistic well-posedness of the nonlinear Schrödinger equations with non-algebraic nonlinearities ⋮ Global dynamics for the stochastic KdV equation with white noise as initial data ⋮ Almost sure global well-posedness for the energy-critical defocusing nonlinear wave equation on \(\mathbb R^d\), \(d=4\) and \(5\) ⋮ On the Probabilistic Cauchy Theory for Nonlinear Dispersive PDEs ⋮ A Pedestrian approach to the invariant Gibbs measures for the 2-\(d\) defocusing nonlinear Schrödinger equations ⋮ Invariant Gibbs measures for the 2-\(d\) defocusing nonlinear wave equations ⋮ On the two-dimensional singular stochastic viscous nonlinear wave equations
Cites Work
- 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
- Equivalence and perpendicularity of Gaussian processes
- Construction of a Gibbs measure associated to the periodic Benjamin-Ono equation
- Global wellposedness of KdV in \(H^{-1}(\mathbb T,\mathbb R)\)
- Random data Cauchy theory for supercritical wave equations. II. A global existence result
- Random data Cauchy theory for supercritical wave equations I: Local theory
- Periodic stochastic Korteweg-de Vries equation with additive space-time white noise
- Invariant measures for the defocusing nonlinear Schrödinger equation
- KdV preserves white noise
- Invariance of the white noise for KdV
- 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
- On the Cauchy and invariant measure problem for the periodic Zakharov system
- Invariant measures for the Gross-Pitaevskii equation
- Statistical mechanics of nonlinear wave equations. IV: Cubic Schrödinger
- Invariant measures for the 2D-defocusing nonlinear Schrödinger equation
- Invariant measures for NLS in infinite volume
- Invariance of the Gibbs measure for the Benjamin-Ono equation
- On the one-dimensional cubic nonlinear Schrödinger equation below \(L^{2}\)
- Probabilistic well-posedness for the cubic wave equation
- Wave turbulence for the BBM equation: stability of a Gaussian statistics under the flow of BBM
- A remark on normal forms and the ``I-method for periodic NLS
- On equivalence of infinite product measures
- Transformations of Wiener integrals under translations
- Remarks on Nonlinear Smoothing under Randomization for the Periodic KdV and the Cubic Szegö Equation
- Global infinite energy solutions for the cubic wave equation
- Almost Sure Existence of Global Weak Solutions for Supercritical Navier--Stokes Equations
- Asymptotic probabilities and differential equations
