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

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Authors

Noguera Salgado, Norman F.
Pastor Ferreira, Ademir

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Abstract

In this work we give a sharp criterion for the global well-posedness, in the energy space, for a system of nonlinear Schr¨odinger 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.

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Global well-posedness, Schrödinger systems, blow up, Ground states solutions

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https://intlpress.com/site/pub/pages/journals/items/dpde/content/vols/0017/0001/a001/index.php

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