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Abstract
In this note, we consider the illposedness issue for the cubic nonlinear Schrödinger equation (NLS) on the circle. In particular, adapting the argument by ChristCollianderTao [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 (fromto)  5384 
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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Dive into the research topics of 'On the illposedness of the cubic nonlinear Schrödinger equation on the circle'. Together they form a unique fingerprint.Projects
 1 Finished

ProbDynDispEq  Probabilistic and Dynamical Study of Nonlinear Dispersive Equations
1/03/15 → 29/02/20
Project: Research