Global Well-Posedness and Scattering for Mass-Critical, Defocusing, Infinite Dimensional Vector-Valued Resonant Nonlinear Schrödinger System

DOI10.1137/17M1131830zbMath1428.35541arXiv1704.08976MaRDI QIDQ4608168

Lifeng Zhao, Kailong Yang

Publication date: 16 March 2018

Published in: SIAM Journal on Mathematical Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1704.08976

zbMATH Keywords

scatteringnonlinear Schrödinger systeminfinite dimensional

Mathematics Subject Classification ID

NLS equations (nonlinear Schrödinger equations) (35Q55)

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Cites Work

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• Dispersive equations and nonlinear waves. Generalized Korteweg-de Vries, nonlinear Schrödinger, wave and Schrödinger maps
• Global solutions for 2D quadratic Schrödinger equations
• Global well-posedness and scattering for the defocusing, \(L^2\)-critical, nonlinear Schrödinger equation when \(d=2\)
• Integrable nonlinear Schrödinger systems and their soliton dynamics
• Global well-posedness, scattering and blow-up for the energy-critical focusing non-linear wave equation
• Scattering theory in the energy space for a class of nonlinear Schrödinger equations
• On scattering for NLS: from Euclidean to hyperbolic space
• Global well-posedness, scattering and blow-up for the energy-critical, focusing, nonlinear Schrö\-dinger equation in the radial case
• Global well-posedness and scattering for the mass critical nonlinear Schrödinger equation with mass below the mass of the ground state
• 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]
• The cubic nonlinear Schrödinger equation in two dimensions with radial data
• Convergence of solutions of H-systems or how to blow bubbles
• The nonlinear Schrödinger equation. Self-focusing and wave collapse
• Global well-posedness and scattering for the defocusing, cubic nonlinear Schrödinger equation when \(n = 3\) via a linear-nonlinear decomposition
• The mass-critical nonlinear Schrödinger equation with radial data in dimensions three and higher
• Global well-posedness and scattering for the energy-critical Schrödinger equation in \(\mathbb R^{3}\)
• Global well-posedness and scattering for the defocusing mass-critical nonlinear Schrödinger equation for radial data in high dimensions
• Global well-posedness and scattering for the defocusing, L2-critical, nonlinear Schrödinger equation when d = 1
• On Scattering for the Quintic Defocusing Nonlinear Schrödinger Equation on R × T²
• Global well-posedness and scattering for the defocusing, $L^{2}$-critical nonlinear Schrödinger equation when $d ≥3$
• The cauchy problem for the critical nonlinear Schrödinger equation in Hs
• Classical Fourier Analysis
• Minimal-mass blowup solutions of the mass-critical NLS
• The focusing energy-critical nonlinear Schrödinger equation in dimensions five and higher
• Bilinear virial identities and applications
• Endpoint Strichartz estimates
• Nonlinear Hyperbolic Equations in Infinite Homogeneous Waveguides
• Small Data Scattering for the Nonlinear Schrödinger Equation on Product Spaces

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