Dynamics of Partial Differential Equations

Volume 17 (2020)

Number 1

On the dynamics of a quadratic Schrödinger system in dimension $n = 5$

Pages: 1 – 17

DOI: https://dx.doi.org/10.4310/DPDE.2020.v17.n1.a1

Authors

Norman Noguera (Instituto de Matemática, Estatística e Computação Científica, UNICAMP, Campinas, SP, Brazil)

Ademir Pastor (Instituto de Matemática, Estatística e Computação Científica, UNICAMP, Campinas, SP, Brazil)

Abstract

In this work we give a sharp criterion for the global well-posedness, in the energy space, for a system of nonlinear Schrödinger equations with quadratic interaction in dimension $n = 5$. The criterion is given in terms of the charge and energy of the ground states associated with the system, which are obtained by minimizing a Weinstein-type functional. The main result is then obtained in view of a sharp Gagliardo–Nirenberg-type inequality.

Keywords

Schrödinger sytems, global well-posedness, blow up, ground states solutions

2010 Mathematics Subject Classification

35A01, 35B44, 35J47, 35Q55

Full Text (PDF format)

N.N. is partially supported by Universidad de Costa Rica, through the OAICE.

A.P. is partially supported by CNPq/Brazil grants 402849/2016-7 and 303098/2016-3.

Received 10 April 2018

Published 18 February 2020