Global well-posedness and scattering for the mass-critical Hartree equation with radial data

Abstract

We establish global well-posedness and scattering for solutions to the mass-critical nonlinear Hartree equation $i{u}_t+\Delta u=\pm (|x{|}^{-2}\ast |u{|}^2)u$ for large spherically symmetric $L_x^2({\mathbb{R}}^d)$ initial data; in the focusing case we require, of course, that the mass is strictly less than that of the ground state.

arXiv comment38 pages, 1 figure

References in corpus (6)

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• Global well-posedness and scattering for the defocusing $H^{\frac{1}{2}}$-subcritical Hartree equation in ${\mathbb{R}}^d$
• Global regularity of wave maps III. Large energy from ${\mathbb{R}}^{1+2}$ to hyperbolic spaces
• On global solution to the Klein-Gordon-Hartree equation below energy space
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• The dynamics of the NLS with the combined terms in five and higher dimensions
• The Defocusing Energy-Critical Wave Equation with a Cubic Convolution
• Global well-posedness for the defocusing Hartree equation with radial data in ${\mathbb{R}}^4$
• The Defocusing Energy-critical Klein-Gordon-Hartree Equation
• Almost sure local wellposedness of energy critical fractional Schrödinger equations with hartree nonlinearity
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• Asymptotically linear solutions in H^1 of the 2-d defocusing nonlinear Schroedinger and Hartree equations
• On the Global Existence and Blowup Phenomena of Schrödinger Equations with Multiple Nonlinearities
• On the blow up phenomenon for the mass critical focusing Hartree equation with inverse-square potential
• Scattering for the focusing ${\dot{H}}^{1/2}$-critical Hartree equation with radial data