Semilinear schrödinger flows on hyperbolic spaces: Scattering in H1

Alexandru D. Ionescu, Gigliola Staffilani

Research output: Contribution to journalArticlepeer-review

28 Scopus citations

Abstract

We prove global well-posedness and scattering in H1 for the defocusing nonlinear Schrödinger equations on the hyperbolic spaces ℍd, d ≥ 2, for exponents. The main unexpected conclusion is scattering to linear solutions in the case of small exponents σ; for comparison, on Euclidean spaces scattering in H1 is not known for any exponent and is known to fail for. Our main ingredients are certain noneuclidean global in time Strichartz estimates and noneuclidean Morawetz inequalities.

Original languageEnglish (US)
Pages (from-to)133-158
Number of pages26
JournalMathematische Annalen
Volume345
Issue number1
DOIs
StatePublished - Jul 2009

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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