Global existence and scattering for the nonlinear Schrödinger equation on Schwarzschild manifolds
نویسنده
چکیده
We consider the nonlinear Schrödinger equation with a pure power repulsive nonlinearity on Schwarzschild manifolds. Equations of this type arise when a nonlinear wave equation on a Schwarzschild manifold is written in Hamiltonian form, cf. [2], [10]. For radial solutions with sufficiently localized initial data, we obtain global existence, L estimates, and the existence and asymptotic completeness of the wave operators. Our approach is based on a dilation identity and global space-time estimates.
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