We study the energy-critical nonlinear wave equation in the presence of an inverse-square potential in dimensions three and four. In the defocussing case, we prove that arbitrary initial data in the energy space lead to global solutions that scatter. In the focusing case, we prove scattering below the ground state threshold.

中文翻译：

---

具有平方反比能的临界能量非线性波动方程

我们研究在尺寸为3和4的平方反比电势下的能量临界非线性波动方程。在散焦情况下，我们证明了能量空间中的任意初始数据会导致分散的全局解决方案。在聚焦情况下，我们证明散射低于基态阈值。