On the ill-posedness of the cubic nonlinear Schrödinger equation on the circle

Tadahiro Oh; Yuzhao Wang

On the ill-posedness of the cubic nonlinear Schrödinger equation on the circle

School of Mathematics

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

Abstract

In this note, we consider the ill-posedness issue for the cubic nonlinear Schrödinger equation (NLS) on the circle. In particular, adapting the argument by Christ-Colliander-Tao [14] to the periodic setting, we exhibit a norm inflation phenomenon for both the usual cubic NLS and the Wick ordered cubic NLS for s≤s_{crit} :=−1/2. We also discuss norm inflation phenomena for general cubic fractional NLS on the circle.

Original language	English
Pages (from-to)	53-84
Number of pages	32
Journal	Analele Ştiinţifice ale Universităţii "Alexandru Ioan Cuza'' din Iaşi - Matematică (Annals of the Alexandru Ioan Cuza University - Mathematics)
Volume	64
Issue number	1
Publication status	Published - 31 Dec 2018

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ProbDynDispEq - Probabilistic and Dynamical Study of Nonlinear Dispersive Equations
Oh, T.
EU government bodies
1/03/15 → 29/02/20
Project: Research

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title = "On the ill-posedness of the cubic nonlinear Schr{\"o}dinger equation on the circle",

abstract = "In this note, we consider the ill-posedness issue for the cubic nonlinear Schr{\"o}dinger equation (NLS) on the circle. In particular, adapting the argument by Christ-Colliander-Tao [14] to the periodic setting, we exhibit a norm inflation phenomenon for both the usual cubic NLS and the Wick ordered cubic NLS for s≤s_{crit} :=−1/2. We also discuss norm inflation phenomena for general cubic fractional NLS on the circle. ",

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On the ill-posedness of the cubic nonlinear Schrödinger equation on the circle. / Oh, Tadahiro; Wang, Yuzhao.

In: Analele Ştiinţifice ale Universităţii "Alexandru Ioan Cuza'' din Iaşi - Matematică (Annals of the Alexandru Ioan Cuza University - Mathematics), Vol. 64, No. 1, 31.12.2018, p. 53-84.

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

TY - JOUR

T1 - On the ill-posedness of the cubic nonlinear Schrödinger equation on the circle

AU - Oh, Tadahiro

AU - Wang, Yuzhao

PY - 2018/12/31

Y1 - 2018/12/31

N2 - In this note, we consider the ill-posedness issue for the cubic nonlinear Schrödinger equation (NLS) on the circle. In particular, adapting the argument by Christ-Colliander-Tao [14] to the periodic setting, we exhibit a norm inflation phenomenon for both the usual cubic NLS and the Wick ordered cubic NLS for s≤s_{crit} :=−1/2. We also discuss norm inflation phenomena for general cubic fractional NLS on the circle.

AB - In this note, we consider the ill-posedness issue for the cubic nonlinear Schrödinger equation (NLS) on the circle. In particular, adapting the argument by Christ-Colliander-Tao [14] to the periodic setting, we exhibit a norm inflation phenomenon for both the usual cubic NLS and the Wick ordered cubic NLS for s≤s_{crit} :=−1/2. We also discuss norm inflation phenomena for general cubic fractional NLS on the circle.

M3 - Article

VL - 64

SP - 53

EP - 84

JO - Analele Ştiinţifice ale Universităţii "Alexandru Ioan Cuza'' din Iaşi - Matematică (Annals of the Alexandru Ioan Cuza University - Mathematics)

JF - Analele Ştiinţifice ale Universităţii "Alexandru Ioan Cuza'' din Iaşi - Matematică (Annals of the Alexandru Ioan Cuza University - Mathematics)

SN - 1221-8421

IS - 1

ER -

On the ill-posedness of the cubic nonlinear Schrödinger equation on the circle

Abstract

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ProbDynDispEq - Probabilistic and Dynamical Study of Nonlinear Dispersive Equations

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