Small data scattering for the nonlinear Schrödinger equation on product spaces

Details Small data scattering for the nonlinear Schrödinger equation on product spaces Small data scattering for the nonlinear Schrödinger equation on product spaces

2010-11-29

arxiv.org/abs/1011.6185v2

Mathematics

Analysis of PDEs

10 pages, slightly revised version, to appear on Comm. PDE

Scientific paper

We consider the cubic nonlinear Schr\"odinger equation, posed on $\R^n\times
M$, where $M$ is a compact Riemannian manifold and $n\geq 2$. We prove that
under a suitable smallness in Sobolev spaces condition on the data there exists
a unique global solution which scatters to a free solution for large times.

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