dc.contributor.author Banica, V. dc.contributor.author Vega, L. dc.date.accessioned 2017-03-13T11:13:16Z dc.date.available 2017-03-13T11:13:16Z dc.date.issued 2017-02-02 dc.identifier.uri http://hdl.handle.net/20.500.11824/652 dc.description.abstract In this note we consider the 1-D cubic Schrödinger equation with data given as small perturbations of a Dirac-$\delta$ function and some other related equations. We first recall that although the problem for this type of data is ill-posed one can use the geometric framework of the Schrödinger map to define the solution beyond the singularity time. Then, we find some natural and well defined geometric quantities that are not regular at time zero. Finally, we make a link between these results and some known phenomena in fluid mechanics that inspired this note. en_US dc.format application/pdf en_US dc.language.iso eng en_US dc.rights Reconocimiento-NoComercial-CompartirIgual 3.0 España en_US dc.rights.uri http://creativecommons.org/licenses/by-nc-sa/3.0/es/ en_US dc.title Singularity formation for the 1-D cubic NLS and the Schrödinger map on $\mathbb{S}^2$ en_US dc.type info:eu-repo/semantics/article en_US dc.identifier.arxiv 1702.01947 dc.relation.publisherversion https://arxiv.org/abs/1702.01947 en_US dc.relation.projectID info:eu-repo/grantAgreement/EC/H2020/669689 en_US dc.relation.projectID ES/1PE/SEV-2013-0323 en_US dc.relation.projectID ES/1PE/MTM2014-53145-P en_US dc.relation.projectID EUS/BERC/BERC.2014-2017 en_US dc.rights.accessRights info:eu-repo/semantics/openAccess en_US dc.type.hasVersion info:eu-repo/semantics/acceptedVersion en_US
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