A new proof of scattering for the 5D radial focusing Hartree equation

Abstract

We revisit the scattering result below the ground state of Y. Gao and H. Wu [Scattering for the focusing ${\dot{\mathrm{H}}}^{\frac{1}{2}}$ -critical Hartree equation in energy space. Nonlinear Anal. 2010;73:1043–1056] on the radial focusing energy-subcritical Hartree equation in d = 5, using the method in Dodson and Murphy [A new proof of scattering below the ground state for the 3D radial focusing cubic NLS. preprint, arXiv:1712.09962]. Using the radial Sobolev embedding and a virial-Morawetz type estimate we can exclude the concentration of mass near the origin instead of using the concentration compactness method in Gao and Wu [Scattering for the focusing ${\dot{\mathrm{H}}}^{\frac{1}{2}}$-critical Hartree equation in energy space. Nonlinear Anal. 2010;73:1043–1056].

Keywords:

• Hartree equation
• scatter
• Morawetz estimate

2010 Mathematics Subject Classifications:

• Primary 35Q55
• Secondary 47J35

Disclosure statement

No potential conflict of interest was reported by the author(s).