Energy scattering for Hartree equations

DOI10.4310/MRL.1999.v6.n1.a8zbMath0949.35104OpenAlexW2031252201MaRDI QIDQ1574688

Kenji Nakanishi

Publication date: 13 August 2000

Published in: Mathematical Research Letters (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.4310/mrl.1999.v6.n1.a8

zbMATH Keywords

scattering operatorsglobal a priori space-time estimateswhole energy space

Mathematics Subject Classification ID

Scattering theory for PDEs (35P25) A priori estimates in context of PDEs (35B45) Schrödinger operator, Schrödinger equation (35J10) (2)-body potential quantum scattering theory (81U05)

Related Items (25)

Analyticity of the scattering operator for semilinear dispersive equations ⋮ Energy-critical Hartree equation with harmonic potential for radial data ⋮ Quadratic Morawetz inequalities and asymptotic completeness in the energy space for nonlinear Schrödinger and Hartree equations ⋮ On blow-up phenomenon of the solution to some wave-Hartree equation in \(d \geq 5\) ⋮ On the Cauchy problem for the Hartree type semilinear Schrödinger equation in the de Sitter spacetime ⋮ Focusing nonlinear Hartree equation with inverse‐square potential ⋮ Global well-posedness for the defocusing Hartree equation with radial data in ℝ4 ⋮ Scattering versus blow-up for the focusing \(L^2\) supercritical Hartree equation ⋮ The defocusing energy-supercritical Hartree equation ⋮ The Cauchy problem for the Hartree equations under random influences ⋮ Global well-posedness and scattering for the energy-critical, defocusing Hartree equation for radial data ⋮ ASYMPTOTICALLY LINEAR SOLUTIONS IN H¹ OF THE 2-D DEFOCUSING NONLINEAR SCHRöDINGER AND HARTREE EQUATIONS ⋮ Energy scattering for a Klein-Gordon equation with a cubic convolution ⋮ Scattering for the focusing \(\dot H^{1/2}\)-critical Hartree equation in energy space ⋮ Remarks on the energy scattering for nonlinear Klein-Gordon and Schrödinger equations ⋮ Global well-posedness and scattering for the defocusing Hartree equation in \(\mathbb R^3\) ⋮ Symmetry and classification of solutions to an integral equation of the Choquard type ⋮ Liouville theorems and classification results for a nonlocal Schrödinger equation ⋮ Remarks on global a priori estimates for the nonlinear Schrödinger equation ⋮ Global well-posedness and scattering for the defocusing \(H^{\frac 1 2}\)-subcritical Hartree equation in \(\mathbb R^d\) ⋮ Scattering Theory Below Energy for a Class of Hartree Type Equations ⋮ Global Well-Posedness and Scattering for the Energy-Critical, Defocusing Hartree Equation in ℝ¹⁺ⁿ ⋮ Time-dependent methods in inverse scattering problems for the Hartree-Fock equation ⋮ Remarks on the repulsive Wigner-Poisson system ⋮ Nonrelativistic limit of scattering theory for nonlinear Klein-Gordon equations

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