A class of coupled Schrödinger equations is investigated. First, in the stationary case, the existence of ground states is obtained and a sharp Gagliardo–Nirenberg inequality is discussed. Second, in the energy critical radial case, global well-posedness and scattering for small data are proved.

中文翻译：

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关于耦合非线性Schrödinger系统

研究了一类耦合的薛定ding方程。首先，在平稳情况下，获得了基态的存在，并讨论了尖锐的Gagliardo-Nirenberg不等式。其次，在能量临界径向情况下，证明了小数据的整体适定性和散射性。