Focusing nonlinear Hartree equation with inverse‐square potential

Yu Chen, Jing Lu and Fanfei Meng

Mathematische Nachrichten, 2020, vol. 293, issue 12, 2271-2298

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 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

Date: 2020
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https://doi.org/10.1002/mana.201900331

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