Scattering of radial solutions for quadratic-type Schrödinger systems in dimension five

Norman Noguera; Ademir Pastor

doi:10.3934/dcds.2021018

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2021, Volume 41, Issue 8: 3817-3836. Doi: 10.3934/dcds.2021018

This issue Previous Article On fair entropy of the tent family Next Article On the splitting method for the nonlinear Schrödinger equation with initial data in $ H^1 $

Scattering of radial solutions for quadratic-type Schrödinger systems in dimension five

Norman Noguera^1, and
Ademir Pastor^2, ,

1.
SM-UCR, Ciudad Universitaria Carlos Monge Alfaro, Departamento de Ciencias Naturales, Apdo: 111-4250, San Ramón, Alajuela, Costa Rica
2.
IMECC-UNICAMP, Rua Sérgio Buarque de Holanda, 651, Cidade Universitária, 13083-859, Campinas, São Paulo, Brazil

^* Corresponding author
^* Corresponding author

Received: August 2020

Early access: January 2021

Published: August 2021

The second author is partially supported by CNPq/Brazil grant 303762/2019-5 and FAPESP/Brazil grant 2019/02512-5

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Abstract

In this paper we study the scattering of radial solutions to a $ l $-component system of nonlinear Schrödinger equations with quadratic-type growth interactions in dimension five. Our approach is based on the recent technique introduced by Dodson and Murphy, which relies on the radial Sobolev embedding and a Morawetz estimate.

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Mathematics Subject Classification: Primary:35Q55, 35B40;Secondary:35A01.

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