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Resolvent and spectral measure on non-trapping asymptotically hyperbolic manifolds III: Global-in-time Strichartz estimates without loss

Chen, Xi

Description

In the present paper, we investigate global-in-time Strichartz estimates without loss on non-trapping asymptotically hyperbolic manifolds. Due to the hyperbolic nature of such manifolds, the set of admissible pairs for Strichartz estimates is much larger than usual. These results generalize the works on hyperbolic space due to Anker–Pierfelice and Ionescu–Staffilani. However, our approach is to employ the spectral measure estimates, obtained in the author's joint work with Hassell, to establish...[Show more]

dc.contributor.authorChen, Xi
dc.date.accessioned2018-01-16T04:35:38Z
dc.identifier.issn0294-1449
dc.identifier.urihttp://hdl.handle.net/1885/139359
dc.description.abstractIn the present paper, we investigate global-in-time Strichartz estimates without loss on non-trapping asymptotically hyperbolic manifolds. Due to the hyperbolic nature of such manifolds, the set of admissible pairs for Strichartz estimates is much larger than usual. These results generalize the works on hyperbolic space due to Anker–Pierfelice and Ionescu–Staffilani. However, our approach is to employ the spectral measure estimates, obtained in the author's joint work with Hassell, to establish the dispersive estimates for truncated/microlocalized Schrödinger propagators as well as the corresponding energy estimates. Compared with hyperbolic space, the crucial point here is to cope with the conjugate points on the manifold. Additionally, these Strichartz estimates are applied to the L² well-posedness and L² scattering for nonlinear Schrödinger equations with power-like nonlinearity and small Cauchy data.
dc.format.mimetypeapplication/pdf
dc.publisherElsevier
dc.rights© 2017 Elsevier B.V.
dc.sourceAnnales de l'Institut Henri Poincare (C) Non Linear Analysis
dc.titleResolvent and spectral measure on non-trapping asymptotically hyperbolic manifolds III: Global-in-time Strichartz estimates without loss
dc.typeJournal article
dc.date.issued2017
local.identifier.ariespublicationu4485658xPUB2064
local.publisher.urlhttps://www.elsevier.com/
local.type.statusAccepted Version
local.contributor.affiliationChen, Xi, Mathematical Sciences Institute, The Australian National University
local.identifier.doi10.1016/j.anihpc.2017.08.003
dcterms.accessRightsOpen Access
dc.provenancehttp://www.sherpa.ac.uk/romeo/issn/0294-1449/..."Author's post-print on open access repository after an embargo period of between 12 months and 48 months" from SHERPA/RoMEO site (as at 12/01/18).
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