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

Zihua Guo; Tadahiro Oh

doi:10.1093/imrn/rnw271

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

Zihua Guo, Tadahiro Oh

School of Mathematics

Research output: Contribution to journal › Article › Research › peer-review

49 Citations (Scopus)

Abstract

We prove non-existence of solutions for the cubic nonlinear Schrödinger equation (NLS) on the circle if initial data belong to H^s(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 language	English
Pages (from-to)	1656-1729
Number of pages	74
Journal	International Mathematics Research Notices
Volume	2018
Issue number	6
DOIs	https://doi.org/10.1093/imrn/rnw271
Publication status	Published - 1 Mar 2018

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title = "Non-existence of solutions for the periodic cubic NLS below L2",

abstract = "We prove non-existence of solutions for the cubic nonlinear Schr{\"o}dinger 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.",

author = "Zihua Guo and Tadahiro Oh",

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AU - Guo, Zihua

AU - Oh, Tadahiro

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N2 - 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.

AB - 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.

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DO - 10.1093/imrn/rnw271

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JO - International Mathematics Research Notices

JF - International Mathematics Research Notices

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

Abstract

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