Dynamics of Partial Differential Equations
Volume 17 (2020)
On the dynamics of a quadratic Schrödinger system in dimension $n = 5$
Pages: 1 – 17
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.
Schrödinger sytems, global well-posedness, blow up, ground states solutions
2010 Mathematics Subject Classification
35A01, 35B44, 35J47, 35Q55
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