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Article Dans Une Revue Geometric And Functional Analysis Année : 2008

Scattering theory for radial nonlinear Schrödinger equations on hyperbolic space

Résumé

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.
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Dates et versions

hal-00084492 , version 1 (07-07-2006)
hal-00084492 , version 2 (19-07-2006)

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Valeria Banica, Rémi Carles, Gigliola Staffilani. Scattering theory for radial nonlinear Schrödinger equations on hyperbolic space. Geometric And Functional Analysis, 2008, 18 (2), pp.367-399. ⟨10.1007/s00039-008-0663-x⟩. ⟨hal-00084492v2⟩
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