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

Noguera Salgado, Norman F.; Pastor Ferreira, Ademir

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

Fecha

2018-10-02

Tipo

artículo original

Autores

Noguera Salgado, Norman F.

Pastor Ferreira, Ademir

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.