On ill-posedness for the one-dimensional periodic cubic Schrodinger equation

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dc.creatorMolinet, Luc
dc.date2008-06-27
dc.date2008-07-02
dc.date.accessioned2026-07-07T09:47:51Z
dc.date.available2026-07-07T09:47:51Z
dc.descriptionWe prove the ill-posedness in $ H^s(\T) $, $s<0$, of the periodic cubic Schrödinger equation in the sense that the flow-map is not continuous from $H^s(\T) $ into itself for any fixed $ t\neq 0 $. This result is slightly stronger than the one obtained by Christ-Colliander-Tao where the discontinuity of the solution map is established. Moreover our proof is different and clarifies the ill-posedness phenomena. Our approach relies on a new result on the behavior of the associated flow-map with respect to the weak topology of $ L^2(\T) $.
dc.descriptionTo appear in Mathematical Research Letters
dc.identifierhttps://arxiv.org/abs/0806.4538
dc.identifierhttp://arxiv.org/abs/0806.4538
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/163994
dc.subjectAnalysis of PDEs
dc.subject35A05, 35Q55
dc.titleOn ill-posedness for the one-dimensional periodic cubic Schrodinger equation
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