On scattering for the defocusing high dimensional inter-critical NLS

Chuanwei Gao; Zehua Zhao

doi:10.1016/j.jde.2019.06.019

On scattering for the defocusing high dimensional inter-critical NLS

Chuanwei Gao
, Zehua Zhao^*

^*Corresponding author for this work

Peking University
Johns Hopkins University

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

7 Citations (Scopus)

Abstract

In this paper, we study the critical norm conjecture for the inter-critical nonlinear Schrödinger equation with critical index s_c satisfying [Formula presented] <s_c<1 when d≥5. Under the assumption of uniform boundedness of the critical norm, we prove the global well-posedness and scattering for the Cauchy problem. We follow the standard ‘Concentration compactness/Rigidity method’ established in [15,16], and treat three scenarios for the critical element respectively. Moreover, double Duhamel method and interaction Morawetz estimate are applied to exclude the critical element.

Original language	English
Pages (from-to)	6198-6215
Number of pages	18
Journal	Journal of Differential Equations
Volume	267
Issue number	11
DOIs	https://doi.org/10.1016/j.jde.2019.06.019
Publication status	Published - 15 Nov 2019
Externally published	Yes

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title = "On scattering for the defocusing high dimensional inter-critical NLS",

abstract = "In this paper, we study the critical norm conjecture for the inter-critical nonlinear Schr{\"o}dinger equation with critical index sc satisfying [Formula presented] c<1 when d≥5. Under the assumption of uniform boundedness of the critical norm, we prove the global well-posedness and scattering for the Cauchy problem. We follow the standard {\textquoteleft}Concentration compactness/Rigidity method{\textquoteright} established in [15,16], and treat three scenarios for the critical element respectively. Moreover, double Duhamel method and interaction Morawetz estimate are applied to exclude the critical element.",

author = "Chuanwei Gao and Zehua Zhao",

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Y1 - 2019/11/15

N2 - In this paper, we study the critical norm conjecture for the inter-critical nonlinear Schrödinger equation with critical index sc satisfying [Formula presented] c<1 when d≥5. Under the assumption of uniform boundedness of the critical norm, we prove the global well-posedness and scattering for the Cauchy problem. We follow the standard ‘Concentration compactness/Rigidity method’ established in [15,16], and treat three scenarios for the critical element respectively. Moreover, double Duhamel method and interaction Morawetz estimate are applied to exclude the critical element.

AB - In this paper, we study the critical norm conjecture for the inter-critical nonlinear Schrödinger equation with critical index sc satisfying [Formula presented] c<1 when d≥5. Under the assumption of uniform boundedness of the critical norm, we prove the global well-posedness and scattering for the Cauchy problem. We follow the standard ‘Concentration compactness/Rigidity method’ established in [15,16], and treat three scenarios for the critical element respectively. Moreover, double Duhamel method and interaction Morawetz estimate are applied to exclude the critical element.

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DO - 10.1016/j.jde.2019.06.019

M3 - Article

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VL - 267

SP - 6198

EP - 6215

JO - Journal of Differential Equations

JF - Journal of Differential Equations

IS - 11

ER -

On scattering for the defocusing high dimensional inter-critical NLS

Abstract

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