Scattering Theory for Radial Nonlinear Schrödinger Equations on Hyperbolic Space

. 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 proo...

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Bibliographic Details
Published in:	Geometric and functional analysis Vol. 18; no. 2; pp. 367 - 399
Main Authors:	Banica, Valeria, Carles, Rémi, Staffilani, Gigliola
Format:	Journal Article
Language:	English
Published:	Basel SP Birkhäuser Verlag Basel 01-07-2008 Springer Verlag
Subjects:	Analysis Analysis of PDEs Mathematics Mathematics and Statistics Nonlinear Schrödinger equations on manifolds asymptotic behavior Strichartz estimates 35P25 35Q55 Morawetz estimates 35B40 58J37
Online Access:	Get full text
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Summary:	. 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.
ISSN:	1016-443X 1420-8970
DOI:	10.1007/s00039-008-0663-x