Focusing nonlinear Hartree equation with inverse-square potential

Yu Chen; Jing Lu; Fanfei Meng

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arXiv · 1907.12757

Focusing nonlinear Hartree equation with inverse-square potential

Yu Chen·Jing Lu·Fanfei Meng

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Abstract

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}.

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Yu Chen, Jing Lu, Fanfei Meng. 2019-07-30. Focusing nonlinear Hartree equation with inverse-square potential. https://arxiv.org/abs/1907.12757

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