Asymptotic stability of small ground states for NLS under random perturbations
DOI10.4171/AIHPC/31MaRDI QIDQ2693537
Publication date: 21 March 2023
Published in: Annales de l'Institut Henri Poincaré. Analyse Non Linéaire (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2012.05878
Asymptotic behavior of solutions to PDEs (35B40) Nonlinear eigenvalue problems and nonlinear spectral theory for PDEs (35P30) Stability in context of PDEs (35B35) Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type (42B10) NLS equations (nonlinear Schrödinger equations) (35Q55) Soliton equations (35Q51) Existence problems for PDEs: global existence, local existence, non-existence (35A01) PDEs with randomness, stochastic partial differential equations (35R60) Time-dependent Schrödinger equations and Dirac equations (35Q41) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02) Harmonic analysis and PDEs (42B37)
Cites Work
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- Global well-posedness of the energy-critical nonlinear Schrödinger equation with small initial data in \(H^1(\mathbb T^3)\)
- Random data Cauchy theory for the generalized incompressible Navier-Stokes equations
- Almost-sure scattering for the radial energy-critical nonlinear wave equation in three dimensions
- Geometric optics and instability for semi-classical Schrödinger equations
- Random data Cauchy theory for supercritical wave equations. II. A global existence result
- Random data Cauchy theory for supercritical wave equations I: Local theory
- Erratum to ``Well-posedness and scattering for the KP-II equation in a critical space [Ann. I. H. Poincaré - AN 26 (3) (2009) 917-941]
- Autour de l'approximation semi-classique. (Around semiclassical approximation)
- On a class of nonlinear Schrödinger equations. I. The Cauchy problem, general case
- On a class of nonlinear Schrödinger equations. II. Scattering theory, general case
- Invariant manifolds for a class of dispersive, Hamiltonian, partial differential equations
- The nonlinear Schrödinger equation with a potential
- Invariant measures for the 2D-defocusing nonlinear Schrödinger equation
- Small data scattering and soliton stability in \(\dot{H}^{-1/6}\) for the quartic KdV equation
- A survey on asymptotic stability of ground states of nonlinear Schrödinger equations. II
- Randomization improved Strichartz estimates and global well-posedness for supercritical data
- Global well-posedness and scattering for the energy-critical Schrödinger equation in \(\mathbb R^{3}\)
- Long time dynamics for the one dimensional non linear Schrödinger equation
- Effective limiting absorption principles, and applications
- Eigenfunction expansions associated with the Schrödinger operators and their applications to scattering theory
- Spectral and scattering theory for Schrödinger operators
- Multichannel nonlinear scattering for nonintegrable equations
- On the probabilistic Cauchy theory of the cubic nonlinear Schrödinger equation on ℝ^{𝕕}, 𝕕≥3
- Nonlinear Resonances with a Potential: Multilinear Estimates and an Application to NLS
- Decay estimates for Schrödinger operators
- Asymptotics, frequency modulation, and low regularity ill-posedness for canonical defocusing equations
- Random data final-state problem for the mass-subcritical NLS in $L^2$
- Strichartz inequalities and the nonlinear Schrodinger equation on compact manifolds
- Large Data Low Regularity Scattering Results for the Wave Equation on the Euclidean Space
- The Focusing Energy-Critical Nonlinear Wave Equation With Random Initial Data
- Almost sure scattering for the 4D energy-critical defocusing nonlinear wave equation with radial data
- On the Probabilistic Cauchy Theory for Nonlinear Dispersive PDEs
- Wiener randomization on unbounded domains and an application to almost sure well-posedness of NLS
- Structure of wave operators for a scaling-critical class of potentials
- Why are solitons stable?
- Stable blowup for the focusing energy critical nonlinear wave equation under random perturbations
- The \(W^{k,p}\)-continuity of wave operators for Schrödinger operators