# American Institute of Mathematical Sciences

October  2021, 20(10): 3637-3654. doi: 10.3934/cpaa.2021124

## Energy scattering for the focusing fractional generalized Hartree equation

 1 Departement of Mathematics, College of Sciences and Arts in Uglat Asugour, Qassim University, Buraydah, Kingdom of Saudi Arabia 2 University of Tunis El Manar, Faculty of Science of Tunis, LR03ES04 partial differential Equations and applications, 2092 Tunis, Tunisia

* Corresponding author

Received  February 2021 Revised  June 2021 Published  October 2021 Early access  July 2021

This note studies the asymptotics of radial global solutions to the non-linear fractional Schrödinger equation
 $i\dot u-(-\Delta)^s u+|u|^{p-2}(I_\alpha *|u|^p)u = 0.$
Indeed, using a new method due to Dodson-Murphy [10], one proves that, in the inter-critical regime, under the ground state threshold, the radial global solutions scatter in the energy space.
Citation: Tarek Saanouni. Energy scattering for the focusing fractional generalized Hartree equation. Communications on Pure and Applied Analysis, 2021, 20 (10) : 3637-3654. doi: 10.3934/cpaa.2021124
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