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.

38 pages, 1 figure

References in corpus (6)

• Global well-posedness, scattering and blow-up for the energy-critical, focusing, non-linear Schrodinger equation in the radial case
• Global well-posedness and scattering for the energy-critical, defocusing Hartree equation for radial data
• The mass-critical nonlinear Schrödinger equation with radial data in dimensions three and higher
• The defocusing energy-critical nonlinear Schrödinger equation in higher dimensions
• Minimal-mass blowup solutions of the mass-critical NLS
• Sharp linear and bilinear restriction estimates for paraboloids in the cylindrically symmetric case

Cited by in corpus (8)

• 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
• Asymptotically linear solutions in H^1 of the 2-d defocusing nonlinear Schroedinger and Hartree equations
• Almost sure local wellposedness of energy critical fractional Schrödinger equations with hartree nonlinearity
• Global well-posedness for the $L^2$ critical Hartree equation on $\bbr^n$, $n\ge 3$
• On the blow up phenomenon for the mass critical focusing Hartree equation with inverse-square potential
• On the Global Existence and Blowup Phenomena of Schrödinger Equations with Multiple Nonlinearities
• Scattering for the focusing ${\dot{H}}^{1/2}$-critical Hartree equation with radial data