Dynamics of subcritical threshold solutions for energy-critical NLS

Qingtang Su; Zehua Zhao

doi:10.4310/DPDE.2023.v20.n1.a3

Dynamics of subcritical threshold solutions for energy-critical NLS

Qingtang Su
, Zehua Zhao

School of Mathematics and Statistics

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

3 Citations (Scopus)

Abstract

In this paper, we study the dynamics of subcritical threshold solutions for focusing energy critical NLS on R^d (d ≥ 5) with nonradial data. This problem with radial assumption was studied by T. Duyckaerts and F. Merle in [19] for d = 3, 4, 5 and later by D. Li and X. Zhang in [25] for d ≥ 6. We gen-eralize the conclusion for the subcritical threshold solutions by removing the radial assumption for d ≥ 5. A key step is to show exponential convergence to the ground state W (x) up to symmetries if the scattering phenomenon does not occur. Remarkably, an interaction Morawetz-type estimate is applied.

Original language	English
Pages (from-to)	37-72
Number of pages	36
Journal	Dynamics of Partial Differential Equations
Volume	20
Issue number	1
DOIs	https://doi.org/10.4310/DPDE.2023.v20.n1.a3
Publication status	Published - 2023

Keywords

energy-critical
focusing NLS
ground state
interaction Morawetz estimate
threshold solution

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10.4310/DPDE.2023.v20.n1.a3

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abstract = "In this paper, we study the dynamics of subcritical threshold solutions for focusing energy critical NLS on Rd (d ≥ 5) with nonradial data. This problem with radial assumption was studied by T. Duyckaerts and F. Merle in [19] for d = 3, 4, 5 and later by D. Li and X. Zhang in [25] for d ≥ 6. We gen-eralize the conclusion for the subcritical threshold solutions by removing the radial assumption for d ≥ 5. A key step is to show exponential convergence to the ground state W (x) up to symmetries if the scattering phenomenon does not occur. Remarkably, an interaction Morawetz-type estimate is applied.",

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TY - JOUR

T1 - Dynamics of subcritical threshold solutions for energy-critical NLS

AU - Su, Qingtang

AU - Zhao, Zehua

PY - 2023

Y1 - 2023

N2 - In this paper, we study the dynamics of subcritical threshold solutions for focusing energy critical NLS on Rd (d ≥ 5) with nonradial data. This problem with radial assumption was studied by T. Duyckaerts and F. Merle in [19] for d = 3, 4, 5 and later by D. Li and X. Zhang in [25] for d ≥ 6. We gen-eralize the conclusion for the subcritical threshold solutions by removing the radial assumption for d ≥ 5. A key step is to show exponential convergence to the ground state W (x) up to symmetries if the scattering phenomenon does not occur. Remarkably, an interaction Morawetz-type estimate is applied.

AB - In this paper, we study the dynamics of subcritical threshold solutions for focusing energy critical NLS on Rd (d ≥ 5) with nonradial data. This problem with radial assumption was studied by T. Duyckaerts and F. Merle in [19] for d = 3, 4, 5 and later by D. Li and X. Zhang in [25] for d ≥ 6. We gen-eralize the conclusion for the subcritical threshold solutions by removing the radial assumption for d ≥ 5. A key step is to show exponential convergence to the ground state W (x) up to symmetries if the scattering phenomenon does not occur. Remarkably, an interaction Morawetz-type estimate is applied.

KW - energy-critical

KW - focusing NLS

KW - ground state

KW - interaction Morawetz estimate

KW - threshold solution

UR - https://www.scopus.com/pages/publications/85144656698

U2 - 10.4310/DPDE.2023.v20.n1.a3

DO - 10.4310/DPDE.2023.v20.n1.a3

M3 - Article

AN - SCOPUS:85144656698

SN - 1548-159X

VL - 20

SP - 37

EP - 72

JO - Dynamics of Partial Differential Equations

JF - Dynamics of Partial Differential Equations

IS - 1

ER -

Dynamics of subcritical threshold solutions for energy-critical NLS

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Keywords

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