Abstract
Abstract We study the nonlinear Schrödinger equation posed on product spaces ℝ n × ℳ k {{\mathbb{R}}^{n}\times{\mathcal{M}}^{k}} , for n ≥ 1 {n\geq 1} and k ≥ 1 {k\geq 1} , with ℳ k {{\mathcal{M}}^{k}} any k-dimensional compact Riemannian manifold. The main results concern global well-posedness and scattering for small data solutions in non-isotropic Sobolev fractional spaces. In the particular case of k = 2 {k=2} , H 1 {H^{1}} -scattering is also obtained.
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