We consider the Cauchy problem for the energy-critical nonlinear Schr\"odinger equation with fractional Laplacian (fNLS) in the radial case. We obtain global well-posedness and scattering in the energy space in the defocusing case, and in the focusing case with energy below the ground state.

中文翻译：

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关于径向情况下能量临界分数薛定谔方程

我们在径向情况下考虑具有分数拉普拉斯算子 (fNLS) 的能量临界非线性 Schr\"odinger 方程的柯西问题。我们在散焦情况下获得能量空间中的全局适定性和散射，在聚焦情况下能量低于基态。