Well-posedness and scattering for the mass-energy NLS on $\mathbf{R}^n\times \mathcal M^k$

Mirko Tarulli

Well-posedness and scattering for the mass-energy NLS on $\mathbf{R}^n\times \mathcal M^k$

Analysis of PDEs 2016-04-01 v2

Authors: Mirko Tarulli

Abstract

We study the nonlinear Schr\"odinger equation posed on product spaces $\mathbf R^n\times \mathcal M^k$ , for $n\geq 1$ and $k\geq1$ , 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 $k=2$ , $H^1$ -scattering is also obtained.

Keywords

nonlinear Schrödinger equation product space compact Riemannian manifold global well-posedness scattering non-isotropic Sobolev space small data solution

Cite

@article{arxiv.1510.01710,
  title  = {Well-posedness and scattering for the mass-energy NLS on $\mathbf{R}^n\times \mathcal M^k$},
  author = {Mirko Tarulli},
  journal= {arXiv preprint arXiv:1510.01710},
  year   = {2016}
}

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