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

2015/08/04 by Tadahiro Oh, Yuzhao Wang, Oh, Tadahiro +1
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Photonic Systems #Nonlinear Waves and Solitons #Numerical methods for differential equations #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.1508.00827

openalex publication_date 2015/08/04 · openalex created_date 2019/04/01 · openalex updated_date 2026/07/28

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 :=- \frac 12. We also discuss norm inflation phenomena for general cubic fractional NLS on the circle.

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