We obtain global well-posedness, scattering, and global L^2(n+2)/(n-2)t,x space-time bounds for energy-space solutions to the energy-critical nonlinear Schrödinger (NLS) equation in \ Rₜ\× \ Rⁿₓ , n\≥ 5
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Monica Vişan (2007) studied this question.
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