Scattering theory for radial nonlinear Schrödinger equations on hyperbolic space

Details Scattering theory for radial nonlinear Schrödinger equations on hyperbolic space Scattering theory for radial nonlinear Schrödinger equations on hyperbolic space

2006-07-07

arxiv.org/abs/math/0607186v2

Mathematics

Analysis of PDEs

Some comments and references added in Section 6

Scientific paper

We study the long time behavior of radial solutions to nonlinear Schr\"{o}dinger 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.

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