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dc.contributor.authorTakaoka, Hideo ( )
dc.date.accessioned2020-06-09T21:15:49Z
dc.date.available2020-06-09T21:15:49Z
dc.date.issued2001-06-05
dc.identifier.citationTakaoka, H. (2001). Global well-posedness for Schrodinger equations with derivative in a nonlinear term and data in low-order Sobolev spaces. Electronic Journal of Differential Equations, 2001(42), pp. 1-23.en_US
dc.identifier.issn1072-6691
dc.identifier.urihttps://digital.library.txstate.edu/handle/10877/11554
dc.description.abstractIn this paper, we study the existence of global solutions to Schrodinger equations in one space dimension with a derivative in a nonlinear term. For the Cauchy problem we assume that the data belongs to a Sobolev space weaker than the finite energy space H1. Global existence for H1 data follows from the local existence and the use of a conserved quantity. For Hs data with s<1, the main idea is to use a conservation law and a frequency decomposition of the Cauchy data then follow the method introduced by Bourgain [3]. Our proof relies on a generalization of the tri-linear estimates associated with the Fourier restriction norm method used in [1,25].en_US
dc.formatText
dc.format.extent23 pages
dc.format.medium1 file (.pdf)
dc.language.isoen_USen_US
dc.publisherTexas State University, Department of Mathematicsen_US
dc.sourceElectronic Journal of Differential Equations, 2001, San Marcos, Texas: Southwest Texas State University and University of North Texas.
dc.subjectNonlinear Schrodinger equationen_US
dc.subjectWell-posednessen_US
dc.titleGlobal Well-posedness for Schrodinger Equations with Derivative in a Nonlinear Term and Data in Low-order Sobolev Spacesen_US
txstate.documenttypeArticle
dc.rights.licenseCreative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.


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