Non-existence of solutions for the periodic cubic NLS below L2

Zihua Guo, Tadahiro Oh

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Abstract

We prove non-existence of solutions for the cubic nonlinear Schrödinger equation (NLS) on the circle if initial data belong to Hs(T)\ L2(T) 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 languageEnglish
Pages (from-to)1656-1729
Number of pages74
JournalInternational Mathematics Research Notices
Volume2018
Issue number6
DOIs
Publication statusPublished - 1 Mar 2018

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