On the global well-posedness of energy-critical Schrödinger equations in curved spaces

Alexandru D. Ionescu, Benoit Pausader, Gigliola Staffilani

Research output: Contribution to journalArticlepeer-review

38 Scopus citations

Abstract

In this paper we present a method to study global regularity properties of solutions of large-data critical Schrödinger equations on certain noncompact Riemannian manifolds. We rely on concentration compactness arguments and a global Morawetz inequality adapted to the geometry of the manifold (in other words we adapt the method of Kenig and Merle to the variable coefficient case), and a good understanding of the corresponding Euclidean problem (a theorem of Colliander, Keel, Staffilani, Takaoka and Tao). As an application we prove global well-posedness and scattering in H1 for the energy-critical defocusing initial-value problem on hyperbolic space ℍ3.

Original languageEnglish (US)
Pages (from-to)705-746
Number of pages42
JournalAnalysis and PDE
Volume5
Issue number4
DOIs
StatePublished - 2012

All Science Journal Classification (ASJC) codes

  • Analysis
  • Numerical Analysis
  • Applied Mathematics

Keywords

  • Energy-critical defocusing nls
  • Global well-posedness
  • Induction on energy
  • Nonlinear schrödinger equation

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