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

Tadahiro Oh^*
, Yuzhao Wang

^*Corresponding author for this work

Mathematics

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

4 Citations (Scopus)

97 Downloads (Pure)

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 := − ½ . 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 Stiintifice ale Universitatii Al I Cuza din Iasi - Matematica
Volume	64
Issue number	1
Publication status	Published - 1 Jan 2018

Keywords

Ill-posedness
Nonlinear Schrödinger equation
Norm inflation

ASJC Scopus subject areas

General Mathematics

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OhWangIasiRevised4Accepted author manuscript, 2.23 MB

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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 ≤ scrit := − ½ . We also discuss norm inflation phenomena for general cubic fractional NLS on the circle. ",

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Oh, T & Wang, Y 2018, 'On the ill-posedness of the cubic nonlinear Schrödinger equation on the circle', Analele Stiintifice ale Universitatii Al I Cuza din Iasi - Matematica, vol. 64, no. 1, pp. 53-84. <http://www.research.ed.ac.uk/portal/en/publications/on-the-illposedness-of-the-cubic-nonlinear-schroedinger-equation-on-the-circle(cc1cc7d8-d610-4589-8765-b9fe597b9e16).html>

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AU - Oh, Tadahiro

AU - Wang, Yuzhao

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Y1 - 2018/1/1

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 ≤ scrit := − ½ . 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 ≤ scrit := − ½ . We also discuss norm inflation phenomena for general cubic fractional NLS on the circle.

KW - Ill-posedness

KW - Nonlinear Schrödinger equation

KW - Norm inflation

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UR - https://www.scopus.com/pages/publications/85061923151

M3 - Article

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SN - 1221-8421

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JO - Analele Stiintifice ale Universitatii Al I Cuza din Iasi - Matematica

JF - Analele Stiintifice ale Universitatii Al I Cuza din Iasi - Matematica

IS - 1

ER -

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

Abstract

Keywords

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