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dc.contributor.advisorOh, Tadahiro
dc.contributor.advisorPocovnicu, Oana
dc.contributor.authorMoşincat, Răzvan Octavian
dc.date.accessioned2018-11-19T13:05:17Z
dc.date.available2018-11-19T13:05:17Z
dc.date.issued2018-11-29
dc.identifier.urihttp://hdl.handle.net/1842/33244
dc.description.abstractThis thesis is concerned with the well-posedness of the one-dimensional derivative non-linear Schrodinger equation (DNLS). In particular, we study the initial-value problem associated to DNLS with low-regularity initial data in two settings: (i) on the torus (namely with the periodic boundary condition) and (ii) on the real line. Our first main goal is to study the global-in-time behaviour of solutions to DNLS in the periodic setting, where global well-posedness is known to hold under a small mass assumption. In Chapter 2, we relax the smallness assumption on the mass and establish global well-posedness of DNLS for smooth initial data. In Chapter 3, we then extend this result for rougher initial data. In particular, we employ the I-method introduced by Colliander, Keel, Staffilani, Takaoka, and Tao and show the global well-posedness of the periodic DNLS at the end-point regularity. In the implementation of the I-method, we apply normal form reductions to construct higher order modified energy functionals. In Chapter 4, we turn our attention to the uniqueness of solutions to DNLS on the real line. By using an infinite iteration of normal form reductions introduced by Guo, Kwon, and Oh in the context of one-dimensional cubic NLS on the torus, we construct solutions to DNLS without using any auxiliary function space. As a result, we prove the unconditional uniqueness of solutions to DNLS on the real line in an almost end-point regularity.en
dc.contributor.sponsorEngineering and Physical Sciences Research Council (EPSRC)en
dc.language.isoenen
dc.publisherThe University of Edinburghen
dc.relation.hasversionR. Mosincat and T. Oh, A remark on global well-posedness of the derivative nonlinear Schrodinger equation on the circle, C.R. Acad. Sci. Paris, Ser. I 353 (2015), pp. 837-841en
dc.relation.hasversionR. Mosincat, Global well-posedness of the derivative nonlinear Schrodinger equation with periodic boundary condition in H 1 2 , J. Differential Equations 263 (2017), 4658-4722.en
dc.subjectnonlinear Schrödinger equationsen
dc.subjectlocal well-posednessen
dc.subjectDNLSen
dc.titleWell-posedness of the one-dimensional derivative nonlinear Schrödinger equationen
dc.typeThesis or Dissertationen
dc.type.qualificationlevelDoctoralen
dc.type.qualificationnamePhD Doctor of Philosophyen


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