Long time dynamics of the 3D radial NLS with the combined terms

Gui Xiang Xu; Jian Wei Yang

doi:10.1007/s10114-016-5401-y

Long time dynamics of the 3D radial NLS with the combined terms

Gui Xiang Xu^*, Jian Wei Yang

^*Corresponding author for this work

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

5 Citations (Scopus)

Abstract

In this paper, we study the scattering and blow-up dichotomy result of the radial solution to nonlinear Schrödinger equation (NLS) with the combined terms (Formula presented.) in energy space H¹(ℝ³). The threshold energy is the energy of the ground state W of the focusing, energy critical NLS, which means that the subcritical perturbation does not affect the determination of threshold, but affects the scattering and blow-up dichotomy result with subcritical threshold energy. This extends algebraic perturbation in a previous work of Miao, Xu and Zhao [Comm. Math. Phys., 318, 767–808 (2013)] to all mass supercritical, energy subcritical perturbation.

Original language	English
Pages (from-to)	521-540
Number of pages	20
Journal	Acta Mathematica Sinica, English Series
Volume	32
Issue number	5
DOIs	https://doi.org/10.1007/s10114-016-5401-y
Publication status	Published - 1 May 2016
Externally published	Yes

Keywords

Blow up
dynamics
nonlinear Schrödinger equation
scattering
threshold energy

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10.1007/s10114-016-5401-y

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title = "Long time dynamics of the 3D radial NLS with the combined terms",

abstract = "In this paper, we study the scattering and blow-up dichotomy result of the radial solution to nonlinear Schr{\"o}dinger equation (NLS) with the combined terms (Formula presented.) in energy space H1(ℝ3). The threshold energy is the energy of the ground state W of the focusing, energy critical NLS, which means that the subcritical perturbation does not affect the determination of threshold, but affects the scattering and blow-up dichotomy result with subcritical threshold energy. This extends algebraic perturbation in a previous work of Miao, Xu and Zhao [Comm. Math. Phys., 318, 767–808 (2013)] to all mass supercritical, energy subcritical perturbation.",

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AU - Xu, Gui Xiang

AU - Yang, Jian Wei

PY - 2016/5/1

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N2 - In this paper, we study the scattering and blow-up dichotomy result of the radial solution to nonlinear Schrödinger equation (NLS) with the combined terms (Formula presented.) in energy space H1(ℝ3). The threshold energy is the energy of the ground state W of the focusing, energy critical NLS, which means that the subcritical perturbation does not affect the determination of threshold, but affects the scattering and blow-up dichotomy result with subcritical threshold energy. This extends algebraic perturbation in a previous work of Miao, Xu and Zhao [Comm. Math. Phys., 318, 767–808 (2013)] to all mass supercritical, energy subcritical perturbation.

AB - In this paper, we study the scattering and blow-up dichotomy result of the radial solution to nonlinear Schrödinger equation (NLS) with the combined terms (Formula presented.) in energy space H1(ℝ3). The threshold energy is the energy of the ground state W of the focusing, energy critical NLS, which means that the subcritical perturbation does not affect the determination of threshold, but affects the scattering and blow-up dichotomy result with subcritical threshold energy. This extends algebraic perturbation in a previous work of Miao, Xu and Zhao [Comm. Math. Phys., 318, 767–808 (2013)] to all mass supercritical, energy subcritical perturbation.

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JO - Acta Mathematica Sinica, English Series

JF - Acta Mathematica Sinica, English Series

IS - 5

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Long time dynamics of the 3D radial NLS with the combined terms

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