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The radial mass-subcritical NLS in negative order Sobolev spaces

Research paper by Rowan Killip, Satoshi Masaki, Jason Murphy, Monica Visan

Indexed on: 18 Apr '18Published on: 18 Apr '18Published in: arXiv - Mathematics - Analysis of PDEs



Abstract

We consider the mass-subcritical NLS in dimensions $d\geq 3$ with radial initial data. In the defocusing case, we prove that any solution that remains bounded in the critical Sobolev space throughout its lifespan must be global and scatter. In the focusing case, we prove the existence of a threshold solution that has a compact flow.