Scattering theory for radial nonlinear Schrodinger equations on hyperbolic space

作者：Banica Valeria^*; Carles Remi; Staffilani Gigliola

来源：Geometric and Functional Analysis, 2008, 18(2): 367-399.

DOI：10.1007/s00039-008-0663-x

• nonlinear Schrodinger equations on manifolds
• asymptotic behavior
• Strichartz estimates
• Morawetz estimates

We study the long-time behavior of radial solutions to nonlinear Schrodinger 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.

• 出版日期2008-7