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We revisit the scattering result below the ground state of Y. Gao and H. Wu [Scattering for the focusing H ˙ 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 H ˙ 1 2 -critical Hartree equation in energy space. Nonlinear Anal. 2010;73:1043–1056]. [ABSTRACT FROM AUTHOR]

In this paper, we simplify the proof of M. Hamano in [13] , scattering theory of the solution to (NLS system) , by using the method from B. Dodson and J. Murphy in [10]. Firstly, we establish a criterion to ensure the solution scatters in H 1 (R 5) × H 1 (R 5). In order to verify the correctness of the condition in scattering criterion, we must exclude the concentration of mass near the origin. The interaction Morawetz estimate and Galilean transform characterize a decay estimate, which implies that the mass of the system cannot be concentrated. [ABSTRACT FROM AUTHOR]

In this paper, we consider the scattering theory of the radial solution to focusing energy‐subcritical Hartree equation with inverse‐square potential in the energy space H1(Rd) using the method from [4]. The main difficulties are due to the fact that the equation is not space‐translation invariant and that the nonlinearity is non‐local. Using the radial Sobolev embedding and a virial‐Morawetz type estimate we can exclude the concentration of mass near the origin. Besides, we can overcome the weak dispersive estimate when a<0, using the dispersive estimate established by [23]. [ABSTRACT FROM AUTHOR]