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Spring 2012 On the one-dimensional cubic nonlinear Schrödinger equation below L2
Tadahiro Oh, Catherine Sulem
Kyoto J. Math. 52(1): 99-115 (Spring 2012). DOI: 10.1215/21562261-1503772


In this paper, we review several recent results concerning well-posedness of the one-dimensional, cubic nonlinear Schrödinger equation (NLS) on the real line R and on the circle T for solutions below the L2-threshold. We point out common results for NLS on R and the so-called Wick-ordered NLS (WNLS) on T, suggesting that WNLS may be an appropriate model for the study of solutions below L2(T). In particular, in contrast with a recent result of Molinet, who proved that the solution map for the periodic cubic NLS equation is not weakly continuous from L2(T) to the space of distributions, we show that this is not the case for WNLS.


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Tadahiro Oh. Catherine Sulem. "On the one-dimensional cubic nonlinear Schrödinger equation below L2." Kyoto J. Math. 52 (1) 99 - 115, Spring 2012.


Published: Spring 2012
First available in Project Euclid: 19 February 2012

zbMATH: 1258.35184
MathSciNet: MR2892769
Digital Object Identifier: 10.1215/21562261-1503772

Primary: 35Q55

Rights: Copyright © 2012 Kyoto University


Vol.52 • No. 1 • Spring 2012
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