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arXiv · 2107.05299

Scattering theory For Quadratic Nonlinear Schr\"odinger System in dimension six

Chuanwei Gao·Fanfei Meng·Chengbin Xu·Jiqiang Zheng
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Abstract

In this paper, we study the solutions to the energy-critical quadratic nonlinear Schr\"odinger system in ${\dot H}^1\times{\dot H}^1$, where the sign of its potential energy can not be determined directly. If the initial data ${\rm u}_0$ is radial or non-radial but satisfies the mass-resonance condition, and its energy is below that of the ground state, using the compactness/rigidity method, we give a complete classification of scattering versus blowing-up dichotomies depending on whether the kinetic energy of ${\rm u}_0$ is below or above that of the ground state.

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Chuanwei Gao, Fanfei Meng, Chengbin Xu, Jiqiang Zheng. 2021-07-12. Scattering theory For Quadratic Nonlinear Schr\"odinger System in dimension six. https://arxiv.org/abs/2107.05299

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