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arXiv · 1509.05822

The energy-critical NLS with inverse-square potential

R. Killip·C. Miao·M. Visan·J. Zhang·J. Zheng
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Abstract

We consider the defocusing energy-critical nonlinear Schr\"odinger equation with inverse-square potential $iu_t = -\Delta u + a|x|^{-2}u + |u|^4u$ in three space dimensions. We prove global well-posedness and scattering for $a>-\frac14 +\frac1{25}$. We also carry out the variational analysis needed to treat the focusing case.

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R. Killip, C. Miao, M. Visan, J. Zhang, J. Zheng. 2015-09-18. The energy-critical NLS with inverse-square potential. https://arxiv.org/abs/1509.05822

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