The energy-critical NLS with inverse-square potential

Rowan Killip; Changxing Miao; Monica Visan; Junyong Zhang; Jiqiang Zheng

doi:10.3934/dcds.2017162

Article Contents

2017, Volume 37, Issue 7: 3831-3866. Doi: 10.3934/dcds.2017162

This issue Previous Article Conjugacies of model sets Next Article Uniformly expanding Markov maps of the real line: Exactness and infinite mixing

The energy-critical NLS with inverse-square potential

1.
Department of Mathematics, UCLA, Los Angeles, CA 90095-1555, USA
2.
Institute of Applied Physics and Computational Mathematics, Beijing 100088, China
3.
Department of Mathematics, Beijing Institute of Technology, Beijing 100081, China
4.
Laboratoire J. A. Dieudonné, Université Nice Sophia-Antipolis, 06108 Nice Cedex 02, France

Received: May 31, 2016

Revised: February 28, 2017

Published: August 2017

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Abstract

We consider the defocusing energy-critical nonlinear Schrödinger equation with inverse-square potential $iu_t = -Δ u + a|x|^{-2}u + |u|^4u$ in three space dimensions. We prove global well-posedness and scattering for $a > - \frac{1}{4} + \frac{1}{{25}}$. We also carry out the variational analysis needed to treat the focusing case.

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Mathematics Subject Classification: Primary: 35Q55; Secondary: 35P25, 47J35.

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