2024-08-052024-08-052018-10-02https://intlpress.com/site/pub/pages/journals/items/dpde/content/vols/0017/0001/a001/index.php2163-78731548-159Xhttps://hdl.handle.net/10669/91940In 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.engacceso abiertoGlobal well-posednessSchrödinger systemsblow upGround states solutionsartículo original10.4310/DPDE.2020.v17.n1.a1