The Sobolev-Morawetz approach for the energy scattering of nonlinear Schrödinger-type equations with radial data

Van Duong Dinh; Sahbi Keraani

doi:10.3934/dcdss.2020407

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2021, Volume 14, Issue 8: 2837-2876. Doi: 10.3934/dcdss.2020407

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The Sobolev-Morawetz approach for the energy scattering of nonlinear Schrödinger-type equations with radial data

Van Duong Dinh^1,2, and
Sahbi Keraani^1, ,

1.
Laboratoire Paul Painlevé UMR 8524, Université de Lille CNRS, 59655 Villeneuve d'Ascq Cedex, France
2.
Department of Mathematics, HCMC University of Pedagogy, 280 An Duong Vuong, Ho Chi Minh, Vietnam

^* Corresponding author: Sahbi Keraani
^* Corresponding author: Sahbi Keraani

Received: December 31, 2019

Revised: May 31, 2020

Early access: July 2020

Published: August 2021

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Abstract

Based on recent works of Dodson-Murphy [12] and Arora-Dodson-Murphy [3], we give a unified approach for the energy scattering with radially symmetric initial data for nonlinear Schrödinger equations and nonlinear Choquard equations in any dimensions $ N\geq 2 $. We also discuss its applications for other Schrödinger-type equations.

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Mathematics Subject Classification: Primary: 35Q55; Secondary: 35P25.

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