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dc.contributor.authorLawrie, Andrew
dc.contributor.authorOh, Sung-Jin
dc.contributor.authorShahshahani, Sohrab
dc.date.accessioned2020-04-27T17:47:37Z
dc.date.available2020-04-27T17:47:37Z
dc.date.issued2016-12
dc.identifier.issn1687-0247
dc.identifier.issn1073-7928
dc.identifier.urihttps://hdl.handle.net/1721.1/124885
dc.description.abstractWe establish global well-posedness and scattering for wave maps from d-dimensional hyperbolic space into Riemannian manifolds of bounded geometry for initial data that is small in the critical Sobolev space for d ≥ 4. The main theorem is proved using the moving frame approach introduced by Shatah and Struwe. However, rather than imposing the Coulomb gauge we formulate the wave maps problem in Tao’s caloric gauge, which is constructed using the harmonic map heat flow. In this setting the caloric gauge has the remarkable property that the main ‘gauged’ dynamic equations reduce to a system of nonlinear scalar wave equations on Hd that are amenable to Strichartz estimates rather than tensorial wave equations (which arise in other gauges such as the Coulomb gauge) for which useful dispersive estimates are not known. This last point makes the heat flow approach crucial in the context of wave maps on curved domains.en_US
dc.description.sponsorshipNational Science Foundation (U.S.) (DMS-1302782)en_US
dc.description.sponsorshipNational Science Foundation (U.S.) (Grant 0932078000)en_US
dc.language.isoen
dc.publisherOxford University Press (OUP)en_US
dc.relation.isversionofhttp://dx.doi.org/10.1093/IMRN/RNW272en_US
dc.rightsCreative Commons Attribution-Noncommercial-Share Alikeen_US
dc.rights.urihttp://creativecommons.org/licenses/by-nc-sa/4.0/en_US
dc.sourcearXiven_US
dc.titleThe Cauchy Problem for Wave Maps on Hyperbolic Space in Dimensions d≥ 4en_US
dc.typeArticleen_US
dc.identifier.citationLawrie, Andrew, et al. “The Cauchy Problem for Wave Maps on Hyperbolic Space in Dimensions d ≥ 4.” International Mathematics Research Notices 2018, 7 (April 2018): 54–2051.en_US
dc.contributor.departmentMassachusetts Institute of Technology. Department of Mathematicsen_US
dc.relation.journalInternational Mathematics Research Noticesen_US
dc.eprint.versionOriginal manuscripten_US
dc.type.urihttp://purl.org/eprint/type/JournalArticleen_US
eprint.statushttp://purl.org/eprint/status/NonPeerRevieweden_US
dc.date.updated2019-11-14T18:23:18Z
dspace.date.submission2019-11-14T18:23:22Z
mit.journal.volume2018en_US
mit.journal.issue6en_US


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