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dc.contributor.authorTao, Terence ( Orcid Icon 0000-0002-0140-7641 )
dc.contributor.authorVisan, Monica ( )
dc.date.accessioned2021-06-22T17:35:49Z
dc.date.available2021-06-22T17:35:49Z
dc.date.issued2005-10-26
dc.identifier.citationTao, T., & Visan, M. (2005). Stability of energy-critical nonlinear Schrodinger equations in high dimensions. Electronic Journal of Differential Equations, 2005(118), pp. 1-28.en_US
dc.identifier.issn1072-6691
dc.identifier.urihttps://digital.library.txstate.edu/handle/10877/13790
dc.description.abstractWe develop the existence, uniqueness, continuity, stability, and scattering theory for energy-critical nonlinear Schrödinger equations in dimensions n ≥ 3, for solutions which have larger, but finite, energy and large, but finite, Strichartz norms. For dimensions n ≤ 6, this theory is a standard extension of the small data well-posedness theory based on iteration in Strichartz spaces. However, in dimensions n > 6 there is an obstruction to this approach because of the subquadratic nature of the nonlinearity (which makes the derivative of the nonlinearity non-Lipschitz). We resolve this by iterating in exotic Strichartz spaces instead. The theory developed here will be applied in a subsequent paper of the second author, [21], to establish global well-posedness and scattering for the defocusing energy-critical equation for large energy data.
dc.formatText
dc.format.extent28 pages
dc.format.medium1 file (.pdf)
dc.language.isoenen_US
dc.publisherTexas State University-San Marcos, Department of Mathematicsen_US
dc.sourceElectronic Journal of Differential Equations, 2005, San Marcos, Texas: Texas State University-San Marcos and University of North Texas.
dc.subjectLocal well-posednessen_US
dc.subjectUniform well-posednessen_US
dc.subjectScattering theoryen_US
dc.subjectStrichartz estimatesen_US
dc.titleStability of energy-critical nonlinear Schrodinger equations in high dimensionsen_US
dc.typepublishedVersion
txstate.documenttypeArticle
dc.rights.licenseCreative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.


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