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Abstract
We prove nonexistence of solutions for the cubic nonlinear Schrödinger equation (NLS) on the circle if initial data belong to H^s(핋)\setminus L^2(핋) for some s∈(−1/8,0). The proof is based on establishing an a priori bound on solutions to a renormalized cubic NLS in negative Sobolev spaces via the short time Fourier restriction norm method.
Original language  English 

Pages (fromto)  16561729 
Number of pages  74 
Journal  International Mathematics Research Notices 
Volume  2018 
Issue number  6 
Early online date  26 Dec 2016 
DOIs  
Publication status  Published  20 Mar 2018 
Keywords
 nonlinear Schrödinger equation
 wellposedness
 illposedness
 short time Fourier restriction norm method
 a priori estimate
 normal form reduction
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Dive into the research topics of 'Nonexistence of solutions for the periodic cubic NLS below L^2'. 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