Energy scattering for the focusing fractional generalized Hartree equation

Tarek Saanouni

doi:10.3934/cpaa.2021124

Article Contents

2021, Volume 20, Issue 10: 3637-3654. Doi: 10.3934/cpaa.2021124 open access

This issue Previous Article Parabolic problems in generalized Sobolev spaces Next Article Robust exponential attractors for singularly perturbed conserved phase-field systems with no growth assumption on the nonlinear term

Energy scattering for the focusing fractional generalized Hartree equation

Tarek Saanouni^1,2, ,

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
^* Corresponding author

Received: January 31, 2021

Revised: May 31, 2021

Early access: July 2021

Published: October 2021

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Abstract

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.

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Mathematics Subject Classification: Primary: 35Q55; Secondary: 35B35.

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References

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