Refined probabilistic global well-posedness for the weakly dispersive NLS
DOI10.1016/j.na.2021.112530zbMath1479.35824arXiv2010.13065OpenAlexW3194544600MaRDI QIDQ2231450
Nickolay Tzvetkov, Chenmin Sun
Publication date: 29 September 2021
Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2010.13065
Fractional derivatives and integrals (26A33) NLS equations (nonlinear Schrödinger equations) (35Q55) Existence problems for PDEs: global existence, local existence, non-existence (35A01) PDEs with randomness, stochastic partial differential equations (35R60) Fractional partial differential equations (35R11) Time-dependent Schrödinger equations and Dirac equations (35Q41) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02) Strong solutions to PDEs (35D35)
Related Items
Cites Work
- Well-posedness and ill-posedness for the cubic fractional Schrödinger equations
- A theory of regularity structures
- Nonlinear fractional Schrödinger equations in one dimension
- Almost sure global well posedness for the radial nonlinear Schrödinger equation on the unit ball I: the 2D case
- On the growth of Sobolev norms of solutions of the fractional defocusing NLS equation on the circle
- Random data Cauchy theory for supercritical wave equations I: Local theory
- Fourier transform restriction phenomena for certain lattice subsets and applications to nonlinear evolution equations. I: Schrödinger equations
- Periodic nonlinear Schrödinger equation and invariant measures
- Strong solutions to the stochastic quantization equations.
- Fractional quantum mechanics and Lévy path integrals
- Invariant measures for the 2D-defocusing nonlinear Schrödinger equation
- On the continuum limit for discrete NLS with long-range lattice interactions
- Optimal local well-posedness for the periodic derivative nonlinear Schrödinger equation
- Almost sure boundedness of iterates for derivative nonlinear wave equations
- A Pedestrian approach to the invariant Gibbs measures for the 2-\(d\) defocusing nonlinear Schrödinger equations
- Probabilistic well-posedness for the cubic wave equation
- Invariant Gibbs measure evolution for the radial nonlinear wave equation on the 3d ball
- Almost sure global well-posedness for the radial nonlinear Schrödinger equation on the unit ball. II: the 3D case
- PARACONTROLLED DISTRIBUTIONS AND SINGULAR PDES
- Almost Sure Global Well-posedness for the Fractional Cubic Schrödinger Equation on the Torus
- Higher order expansions for the probabilistic local Cauchy theory of the cubic nonlinear Schrödinger equation on ℝ³
- Almost Sure Local Well-Posedness for a Derivative Nonlinear Wave Equation
- Remarks on the Gibbs measures for nonlinear dispersive equations
- Gibbs Measure Dynamics for the Fractional NLS
- Solving the 4NLS with white noise initial data
