The energy-critical NLS with inverse-square potential

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

doi:10.3934/dcds.2017162

The energy-critical NLS with inverse-square potential

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

School of Mathematics and Statistics

Research output: Contribution to journal › Article › peer-review

52 Citations (Scopus)

Abstract

We consider the defocusing energy-critical nonlinear Schrödinger equation with inverse-square potential {equation presented} in three space dimensions. We prove global well-posedness and scattering for {equation presented} . We also carry out the variational analysis needed to treat the focusing case.

Original language	English
Pages (from-to)	3831-3866
Number of pages	36
Journal	Discrete and Continuous Dynamical Systems
Volume	37
Issue number	7
DOIs	https://doi.org/10.3934/dcds.2017162
Publication status	Published - Jul 2017

Keywords

Concentration compactness
Inverse-square potential
Nonlinear Schrödinger equation
Scattering

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Killip, R., Miao, C., Visan, M., Zhang, J., & Zheng, J. (2017). The energy-critical NLS with inverse-square potential. Discrete and Continuous Dynamical Systems, 37(7), 3831-3866. https://doi.org/10.3934/dcds.2017162

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title = "The energy-critical NLS with inverse-square potential",

abstract = "We consider the defocusing energy-critical nonlinear Schr{\"o}dinger equation with inverse-square potential {equation presented} in three space dimensions. We prove global well-posedness and scattering for {equation presented} . We also carry out the variational analysis needed to treat the focusing case.",

keywords = "Concentration compactness, Inverse-square potential, Nonlinear Schr{\"o}dinger equation, Scattering",

author = "Rowan Killip and Changxing Miao and Monica Visan and Junyong Zhang and Jiqiang Zheng",

year = "2017",

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AU - Killip, Rowan

AU - Miao, Changxing

AU - Visan, Monica

AU - Zhang, Junyong

AU - Zheng, Jiqiang

PY - 2017/7

Y1 - 2017/7

N2 - We consider the defocusing energy-critical nonlinear Schrödinger equation with inverse-square potential {equation presented} in three space dimensions. We prove global well-posedness and scattering for {equation presented} . We also carry out the variational analysis needed to treat the focusing case.

AB - We consider the defocusing energy-critical nonlinear Schrödinger equation with inverse-square potential {equation presented} in three space dimensions. We prove global well-posedness and scattering for {equation presented} . We also carry out the variational analysis needed to treat the focusing case.

KW - Concentration compactness

KW - Inverse-square potential

KW - Nonlinear Schrödinger equation

KW - Scattering

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JO - Discrete and Continuous Dynamical Systems

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The energy-critical NLS with inverse-square potential

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Keywords

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