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Focusing nonlinear Hartree equation with inverse-square potential

Authors :
Chen, Yu
Lu, Jing
Meng, Fanfei
Publication Year :
2019

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}.<br />Comment: 27 pages

Details

Database :
arXiv
Publication Type :
Report
Accession number :
edsarx.1907.12757
Document Type :
Working Paper