Solutions to the energy-critical NLS with repulsive inverse-square potential below the ground-state kinetic threshold are global and scatter to zero.
Dodson,Global well-posedness and scattering for the focusing, energy-critical nonlinear Schr¨ odinger problem in dimensiond= 4for initial data below a ground state threshold.Ann
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Threshold Scattering for the Energy-Critical NLS with a Repulsive Inverse Square Potential
Solutions to the energy-critical NLS with repulsive inverse-square potential below the ground-state kinetic threshold are global and scatter to zero.