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arXiv · 1702.04064

Scattering in $H^1$ for the intercritical NLS with an inverse-square potential

Jing Lu·Changxing Miao·Jason Murphy
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Abstract

We study the nonlinear Schr\"odinger equation with an inverse-square potential in dimensions $3\leq d \leq 6$. We consider both focusing and defocusing nonlinearities in the mass-supercritical and energy-subcritical regime. In the focusing case, we prove a scattering/blowup dichotomy below the ground state. In the defocusing case, we prove scattering in $H^1$ for arbitrary data.

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Jing Lu, Changxing Miao, Jason Murphy. 2017-02-14. Scattering in $H^1$ for the intercritical NLS with an inverse-square potential. https://arxiv.org/abs/1702.04064

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