Well-posedness and scattering for the mass-energy NLS on Rⁿ× \mathcal M^k

2015/10/06 by Tarulli, Mirko
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1510.01710

Abstract

We study the nonlinear Schrödinger equation posed on product spaces \mathbf Rⁿ× \mathcal M^k, for n≥ 1 and k≥1, with \mathcal M^k any k-dimensional compact Riemaniann 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, H¹-scattering is also obtained.

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