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 $H^{1}(\mathbb{R}^d)$ using the method from \cite{Dodson2016}. The main difficulties are the equation is \emph{not} space-translation invariant and 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 \cite{zheng}.

中文翻译：

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具有平方反比势的聚焦非线性 Hartree 方程

在本文中，我们考虑了能量空间 $H^{1}(\mathbb{R}^d)$ 中的聚焦能量次临界 Hartree 方程的径向解的散射理论，该方程的能量空间 $H^{1}(\mathbb{R}^d)$引用{Dodson2016}。主要困难是方程是 \emph{not} 空间平移不变性，非线性是非局部的。使用径向 Sobolev 嵌入和 virial-Morawetz 类型估计，我们可以排除原点附近的质量浓度。此外，当 $a<0$ 时，我们可以克服弱色散估计，使用 \cite{zheng} 建立的色散估计。