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arXiv · 1810.01390

On the dynamics of a quadratic Schr\"odinger system in dimension $n=5$

Norman Noguera·Ademir Pastor
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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 $n=5$. 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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Norman Noguera, Ademir Pastor. 2018-10-02. On the dynamics of a quadratic Schr\"odinger system in dimension $n=5$. https://arxiv.org/abs/1810.01390

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