Almost sure well-posedness of the cubic nonlinear Schrödinger equation below \(L^{2}(\mathbb{T})\)
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Publication:408109
DOI10.1215/00127094-1507400zbMath1260.35199arXiv0904.2820OpenAlexW1965612019MaRDI QIDQ408109
Tadahiro Oh, James E. Colliander
Publication date: 29 March 2012
Published in: Duke Mathematical Journal (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/0904.2820
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Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Invariant Gibbs measures and a.s. global well posedness for coupled KdV systems.
- Modulation spaces, Wiener amalgam spaces, and Brownian motions
- An instability property of the nonlinear Schrödinger equation on \(S^d\)
- Construction of a Gibbs measure associated to the periodic Benjamin-Ono equation
- Random data Cauchy theory for supercritical wave equations. II. A global existence result
- Random data Cauchy theory for supercritical wave equations I: Local theory
- Invariant measures for the defocusing nonlinear Schrödinger equation
- KdV preserves white noise
- On ill-posedness for the one-dimensional periodic cubic Schrödinger equation
- Random data Cauchy problem for supercritical Schrödinger equations
- 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. I: Schrödinger equations
- Periodic nonlinear Schrödinger equation and invariant measures
- On the Cauchy and invariant measure problem for the periodic Zakharov system
- On the Cauchy problem for the Zakharov system
- On the ill-posedness of some canonical dispersive equations.
- Invariant measures for the 2D-defocusing nonlinear Schrödinger equation
- Statistical mechanics of the nonlinear Schrödinger equation.
- On the one-dimensional cubic nonlinear Schrödinger equation below \(L^{2}\)
- A priori bounds and weak solutions for the nonlinear Schrödinger equation in Sobolev spaces of negative order
- Invariant measures for the nonlinear Schrödinger equation on the disc
- Invariance of the Gibbs Measure for the Schrödinger–Benjamin–Ono System
- White noise for KdV and mKdV on the circle
- Remarks on Nonlinear Smoothing under Randomization for the Periodic KdV and the Cubic Szegö Equation
- Low Regularity Local Well-Posedness of the Derivative Nonlinear Schrödinger Equation with Periodic Initial Data
- An invariant measure for a nonlinear wave equation
- Gaussian Hilbert Spaces
- Asymptotics, frequency modulation, and low regularity ill-posedness for canonical defocusing equations
- BILINEAR ESTIMATES AND APPLICATIONS TO NONLINEAR WAVE EQUATIONS
- A Priori Bounds for the 1D Cubic NLS in Negative Sobolev Spaces
- Invariant Measure for a Three Dimensional Nonlinear Wave Equation
- Korteweg-de Vries and nonlinear Schrödinger equations: qualitative theory
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