article published yes Rowan Killip author Jason Murphy author Monica Visan author 056daca0-b8d1-11f0-964f-f91054abf8ca Jiqiang Zheng author We consider the focusing cubic nonlinear Schrödinger 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. Khayyam Publishing2017 eng 0893-4983 1603.0891210.57262/die/1487386822 303/4161-206 yes Killip R, Murphy J, Vişan M, Zheng J. The focusing cubic NLS with inverse-square potential in three space dimensions. <i>Differential and Integral Equations</i>. 2017;30(3/4):161-206. doi:<a href="https://doi.org/10.57262/die/1487386822">10.57262/die/1487386822</a> Killip, Rowan, et al. “The Focusing Cubic NLS with Inverse-Square Potential in Three Space Dimensions.” <i>Differential and Integral Equations</i>, vol. 30, no. 3/4, Khayyam Publishing, 2017, pp. 161–206, doi:<a href="https://doi.org/10.57262/die/1487386822">10.57262/die/1487386822</a>. R. Killip, J. Murphy, M. Vişan, J. Zheng, Differential and Integral Equations 30 (2017) 161–206. Killip, R., Murphy, J., Vişan, M., &#38; Zheng, J. (2017). The focusing cubic NLS with inverse-square potential in three space dimensions. <i>Differential and Integral Equations</i>. Khayyam Publishing. <a href="https://doi.org/10.57262/die/1487386822">https://doi.org/10.57262/die/1487386822</a> Killip, Rowan, Jason Murphy, Monica Vişan, and Jiqiang Zheng. “The Focusing Cubic NLS with Inverse-Square Potential in Three Space Dimensions.” <i>Differential and Integral Equations</i>. Khayyam Publishing, 2017. <a href="https://doi.org/10.57262/die/1487386822">https://doi.org/10.57262/die/1487386822</a>. Killip R, Murphy J, Vişan M, Zheng J. 2017. The focusing cubic NLS with inverse-square potential in three space dimensions. Differential and Integral Equations. 30(3/4), 161–206. R. Killip, J. Murphy, M. Vişan, and J. Zheng, “The focusing cubic NLS with inverse-square potential in three space dimensions,” <i>Differential and Integral Equations</i>, vol. 30, no. 3/4. Khayyam Publishing, pp. 161–206, 2017. 220882026-06-19T08:47:48Z2026-07-01T12:42:38Z