On Scattering for Nls: from Euclidean to Hyperbolic Space
نویسنده
چکیده
We prove asymptotic completeness in the energy space for the nonlinear Schrödinger equation posed on hyperbolic space Hn in the radial case, for n > 4, and any energy-subcritical, defocusing, power nonlinearity. The proof is based on simple Morawetz estimates and weighted Strichartz estimates. We investigate the same question on spaces which kind of interpolate between Euclidean space and hyperbolic space, showing that the family of short range nonlinearities becomes larger and larger as the space approaches the hyperbolic space. Finally, we describe the large time behavior of radial solutions to the free dynamics.
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تاریخ انتشار 2008