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arXiv · 1603.08912

The focusing cubic NLS with inverse-square potential in three space dimensions

Rowan Killip·Jason Murphy·Monica Visan·Jiqiang Zheng
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Abstract

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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Rowan Killip, Jason Murphy, Monica Visan, Jiqiang Zheng. 2016-03-29. The focusing cubic NLS with inverse-square potential in three space dimensions. https://arxiv.org/abs/1603.08912

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