On the dynamics of a quadratic Schrödinger system in dimension n = 5
Fecha
2018-10-02
Autores
Noguera Salgado, Norman F.
Pastor Ferreira, Ademir
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Resumen
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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Palabras clave
Global well-posedness, Schrödinger systems, blow up, Ground states solutions
Citación
https://intlpress.com/site/pub/pages/journals/items/dpde/content/vols/0017/0001/a001/index.php