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

Published 4 Aug 2015 in math.AP | (1508.00827v3)

Abstract: In this note, we consider the ill-posedness issue for the cubic nonlinear Schr\"odinger 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 $s \leq s_\text{crit} :=- \frac 12$. We also discuss norm inflation phenomena for general cubic fractional NLS on the circle.

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Authors (2)

  1. Tadahiro Oh 
  2. Yuzhao Wang 

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