We consider the defocusing energy-critical nonlinear Schrödinger equation with inverse-square potential iuₜ = -Δ u + a|x|⁻²u + |u|⁴u in three space dimensions. We prove global well-posedness and scattering for a > - 1/4 + 125. We also carry out the variational analysis needed to treat the focusing case.
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Killip et al. (2017) studied this question.
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