Well-posedness for energy-critical nonlinear Schrödinger equation on waveguide manifold

Xing Cheng; Zehua Zhao; Jiqiang Zheng

doi:10.1016/j.jmaa.2020.124654

Well-posedness for energy-critical nonlinear Schrödinger equation on waveguide manifold

Xing Cheng
, Zehua Zhao^*
, Jiqiang Zheng

^*Corresponding author for this work

Hohai University
University of Maryland, College Park
IAPCM

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

19 Citations (Scopus)

Abstract

In this article, we utilize the scale-invariant Strichartz estimate on waveguide which is recently developed by Barron [1] based on Bourgain-Demeter l² decoupling method [3] to give a unified and simpler treatment of well-posedness results for energy critical nonlinear Schrödinger equation on waveguide when the whole dimension is three and four. The tori analogue is discussed and proved by Killip-Visan [30]. At last, we give some comments on long time dynamics of NLS with large data in the setting of waveguide.

Original language	English
Article number	124654
Journal	Journal of Mathematical Analysis and Applications
Volume	494
Issue number	2
DOIs	https://doi.org/10.1016/j.jmaa.2020.124654
Publication status	Published - 15 Feb 2021
Externally published	Yes

Keywords

Bilinear estimate
Decoupling method
Nonlinear Schrödinger equation
Strichartz estimate
Waveguide manifold
Well-posedness

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10.1016/j.jmaa.2020.124654

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title = "Well-posedness for energy-critical nonlinear Schr{\"o}dinger equation on waveguide manifold",

abstract = "In this article, we utilize the scale-invariant Strichartz estimate on waveguide which is recently developed by Barron [1] based on Bourgain-Demeter l2 decoupling method [3] to give a unified and simpler treatment of well-posedness results for energy critical nonlinear Schr{\"o}dinger equation on waveguide when the whole dimension is three and four. The tori analogue is discussed and proved by Killip-Visan [30]. At last, we give some comments on long time dynamics of NLS with large data in the setting of waveguide.",

keywords = "Bilinear estimate, Decoupling method, Nonlinear Schr{\"o}dinger equation, Strichartz estimate, Waveguide manifold, Well-posedness",

author = "Xing Cheng and Zehua Zhao and Jiqiang Zheng",

note = "Publisher Copyright: {\textcopyright} 2020",

year = "2021",

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day = "15",

doi = "10.1016/j.jmaa.2020.124654",

language = "English",

volume = "494",

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T1 - Well-posedness for energy-critical nonlinear Schrödinger equation on waveguide manifold

AU - Cheng, Xing

AU - Zhao, Zehua

AU - Zheng, Jiqiang

PY - 2021/2/15

Y1 - 2021/2/15

N2 - In this article, we utilize the scale-invariant Strichartz estimate on waveguide which is recently developed by Barron [1] based on Bourgain-Demeter l2 decoupling method [3] to give a unified and simpler treatment of well-posedness results for energy critical nonlinear Schrödinger equation on waveguide when the whole dimension is three and four. The tori analogue is discussed and proved by Killip-Visan [30]. At last, we give some comments on long time dynamics of NLS with large data in the setting of waveguide.

AB - In this article, we utilize the scale-invariant Strichartz estimate on waveguide which is recently developed by Barron [1] based on Bourgain-Demeter l2 decoupling method [3] to give a unified and simpler treatment of well-posedness results for energy critical nonlinear Schrödinger equation on waveguide when the whole dimension is three and four. The tori analogue is discussed and proved by Killip-Visan [30]. At last, we give some comments on long time dynamics of NLS with large data in the setting of waveguide.

KW - Bilinear estimate

KW - Decoupling method

KW - Nonlinear Schrödinger equation

KW - Strichartz estimate

KW - Waveguide manifold

KW - Well-posedness

UR - https://www.scopus.com/pages/publications/85091916903

U2 - 10.1016/j.jmaa.2020.124654

DO - 10.1016/j.jmaa.2020.124654

M3 - Article

AN - SCOPUS:85091916903

SN - 0022-247X

VL - 494

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

IS - 2

M1 - 124654

ER -

Well-posedness for energy-critical nonlinear Schrödinger equation on waveguide manifold

Abstract

Keywords

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