Geometric and Functional Analysis

, Volume 18, Issue 2, pp 367–399

Scattering Theory for Radial Nonlinear Schrödinger Equations on Hyperbolic Space

  • Valeria Banica
  • Rémi Carles
  • Gigliola Staffilani
Article

DOI: 10.1007/s00039-008-0663-x

Cite this article as:
Banica, V., Carles, R. & Staffilani, G. GAFA Geom. funct. anal. (2008) 18: 367. doi:10.1007/s00039-008-0663-x

Abstract.

We study the long-time behavior of radial solutions to nonlinear Schrödinger equations on hyperbolic space. We show that the usual distinction between short-range and long-range nonlinearity is modified: the geometry of the hyperbolic space makes every power-like nonlinearity short range. The proofs rely on weighted Strichartz estimates, which imply Strichartz estimates for a broader family of admissible pairs, and on Morawetz-type inequalities. The latter are established without symmetry assumptions.

Keywords and phrases:

Nonlinear Schrödinger equations on manifolds asymptotic behavior Strichartz estimates Morawetz estimates 

AMS Mathematics Subject Classification:

35B40 35P25 35Q55 58J37 

Copyright information

© Birkhaeuser 2008

Authors and Affiliations

  • Valeria Banica
    • 1
  • Rémi Carles
    • 2
  • Gigliola Staffilani
    • 3
  1. 1.Département de MathématiquesUniversité d’EvryEvryFrance
  2. 2.CNRS & Université Montpellier 2, Mathématiques, CC 051Montpellier cedex 5France
  3. 3.MITCambridgeUSA

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