Scattering theory for radial nonlinear Schr\"{o}dinger equations on hyperbolic space
Analysis of PDEs
2016-08-16 v2
Abstract
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.
Cite
@article{arxiv.math/0607186,
title = {Scattering theory for radial nonlinear Schr\"{o}dinger equations on hyperbolic space},
author = {Valeria Banica and Rémi Carles and Gigliola Staffilani},
journal= {arXiv preprint arXiv:math/0607186},
year = {2016}
}
Comments
Some comments and references added in Section 6