On scattering for the defocusing high dimensional inter-critical NLS

DOI10.1016/j.jde.2019.06.019zbMath1428.35510arXiv1809.04211OpenAlexW2964081768MaRDI QIDQ2323827

Chuanwei Gao, Zehua Zhao

Publication date: 12 September 2019

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1809.04211

Mathematics Subject Classification ID

Scattering theory for PDEs (35P25) NLS equations (nonlinear Schrödinger equations) (35Q55) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Time-dependent Schrödinger equations and Dirac equations (35Q41) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02)

Related Items

Standing waves with prescribed \(L^2\)-norm to nonlinear Schrödinger equations with combined inhomogeneous nonlinearities ⋮ Global well-posedness and scattering for the defocusing \(\dot{H}^{1/2}\)-critical nonlinear Schrödinger equation in \(\mathbb{R}^2\)

Cites Work

• Unnamed Item
• The defocusing \(\dot{H}^{1/2}\)-critical NLS in high dimensions
• The defocusing energy-supercritical NLS in four space dimensions
• Global well-posedness and scattering for the defocusing, \(L^2\)-critical, nonlinear Schrödinger equation when \(d=2\)
• The radial defocusing energy-supercritical NLS in dimension four
• The defocusing quintic NLS in four space dimensions
• 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
• Partial differential equations. I: Basic theory
• The cubic nonlinear Schrödinger equation in two dimensions with radial data
• Dispersion of small amplitude solutions of the generalized Korteweg-de Vries equation
• The defocusing energy-critical nonlinear Schrödinger equation in higher dimensions
• 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 \(\dot H^s\)-critical NLS
• 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 higher-dimensional energy-critical nonlinear Schrö\-dinger equation for radial data
• Global well-posedness and scattering for the defocusing, L2-critical, nonlinear Schrödinger equation when d = 1
• 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
• Minimal-mass blowup solutions of the mass-critical NLS
• Global well-posedness and scattering for the defocusing energy-critical nonlinear Schrödinger equation in R 1+4
• Scattering for 𝐻̇^{1/2} bounded solutions to the cubic, defocusing NLS in 3 dimensions
• The focusing energy-critical nonlinear Schrödinger equation in dimensions five and higher
• Energy-Supercritical NLS: Critical[Hdot^s-Bounds Imply Scattering]
• Bilinear virial identities and applications
• Global wellposedness of defocusing critical nonlinear Schrödinger equation in the radial case
• On nonlinear schrödinger equations
• Global existence and scattering for rough solutions of a nonlinear Schrödinger equation on ℝ³
• The Radial Defocusing Nonlinear Schrödinger Equation in Three Space Dimensions
• Intercritical NLS: Critical $\dot{H}^s$-Bounds Imply Scattering
• The Nonlinear Schrödinger Equation with Combined Power-Type Nonlinearities
• Improved Interaction Morawetz Inequalities for the Cubic Nonlinear Schrödinger Equation on ℝ2