Global well-posedness and scattering for the energy-critical, defocusing Hartree equation for radial data

Abstract

We consider the defocusing, ${\dot{H}}^1$-critical Hartree equation for the radial data in all dimensions $(n\ge 5)$. We show the global well-posedness and scattering results in the energy space. The new ingredient in this paper is that we first take advantage of the term $-{\int }_I{\int }_{|x|\le A|I{|}^{1/2}}|u{|}^2\Delta (\frac{1}{|x|})dxdt$ in the localized Morawetz identity to rule out the possibility of energy concentration, instead of the classical Morawetz estimate dependent of the nonlinearity.

23 pages, 1 figure

References in corpus (3)

• Global well-posedness, scattering and blow-up for the energy-critical, focusing, non-linear Schrodinger equation in the radial case
• The defocusing energy-critical nonlinear Schrödinger equation in higher dimensions
• Global well-posedness and scattering for the energy-critical nonlinear Schrödinger equation in R^3

Cited by in corpus (7)

• 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 ${\mathbb{R}}^d$
• Almost sure local wellposedness of energy critical fractional Schrödinger equations with hartree nonlinearity
• Global existence and blowup for Choquard equations with an inverse-square potential
• Local existence and uniqueness for the frictional Newton-Schroedinger equation in three dimensions
• Scattering for the focusing ${\dot{H}}^{1/2}$-critical Hartree equation with radial data
• On the blow up phenomenon for the mass critical focusing Hartree equation with inverse-square potential