Global Well-Posedness and Scattering for the Energy-Critical, Defocusing Hartree Equation in ℝ1+n

DOI10.1080/03605302.2010.531073zbMath1252.35235arXiv0707.3254OpenAlexW3105823658MaRDI QIDQ3104531

Lifeng Zhao, Gui Xiang Xu, Chang Xing Miao

Publication date: 14 December 2011

Published in: Communications in Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0707.3254

zbMATH Keywords

global well-posednessHartree equationfrequency-localized interaction Morawetz estimateminimal energy blow-up solutions

Mathematics Subject Classification ID

NLS equations (nonlinear Schrödinger equations) (35Q55) PDEs in connection with quantum mechanics (35Q40) Nonlinear evolution equations (47J35) Blow-up in context of PDEs (35B44)

Related Items (25)

The focusing energy-critical Hartree equation ⋮ Energy-critical Hartree equation with harmonic potential for radial data ⋮ On blow-up phenomenon of the solution to some wave-Hartree equation in \(d \geq 5\) ⋮ Scattering versus blow-up beyond the threshold for the focusing Choquard equation ⋮ Energy scattering of a generalized Davey-Stewartson system in three dimension ⋮ On the Cauchy problem for the Hartree type semilinear Schrödinger equation in the de Sitter spacetime ⋮ A new proof of scattering for the 5D radial focusing Hartree equation ⋮ Initial boundary value problem for a class of wave equations of Hartree type ⋮ Energy scattering of a modified Davey–Stewartson system in three dimensions ⋮ Classification of nonnegative solutions to a bi-harmonic equation with Hartree type nonlinearity ⋮ Global well-posedness for the defocusing Hartree equation with radial data in ℝ4 ⋮ Quantified hydrodynamic limits for Schrödinger-type equations without the nonlinear potential ⋮ The defocusing energy-supercritical Hartree equation ⋮ Scattering for focusing combined power-type NLS ⋮ The Cauchy problem for the Hartree equations under random influences ⋮ Small data global well‐posedness for the nonlinear wave equation with nonlocal nonlinearity ⋮ Scattering theory for the defocusing energy-supercritical nonlinear wave equation with a convolution ⋮ Energy scattering for a Klein-Gordon equation with a cubic convolution ⋮ Minimal mass non-scattering solutions of the focusing \(L^2\)-critical Hartree equations with radial data ⋮ An alternative approach to regularity for the Navier-Stokes equations in critical spaces ⋮ Global well-posedness and scattering for the defocusing Hartree equation in \(\mathbb R^3\) ⋮ Global well-posedness and scattering for the mass-critical Hartree equation with radial data ⋮ Global well-posedness and scattering for the defocusing \(H^{\frac 1 2}\)-subcritical Hartree equation in \(\mathbb R^d\) ⋮ Minimal blow-up initial data for potential blow-up solutions to inter-critical Schrödinger equations ⋮ Sharp threshold for scattering of a generalized Davey-Stewartson system in three dimension

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