On the dynamics of a quadratic Schr\"odinger system in dimension $n=5$
Analysis of PDEs
2018-10-03 v1
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 . 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.
Keywords
Cite
@article{arxiv.1810.01390,
title = {On the dynamics of a quadratic Schr\"odinger system in dimension $n=5$},
author = {Norman Noguera and Ademir Pastor},
journal= {arXiv preprint arXiv:1810.01390},
year = {2018}
}