The focusing cubic NLS with inverse-square potential in three space dimensions
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cubicfocusingdimensionsinverse-squarepotentialspacethreethreshold
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We consider the focusing cubic nonlinear Schr\"odinger equation with inverse-square potential in three space dimensions. We identify a sharp threshold between scattering and blowup, establishing a result analogous to that of Duyckaerts, Holmer, and Roudenko for the standard focusing cubic NLS. We also prove failure of uniform space-time bounds at the threshold.
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