ABSTRACT
We show that assuming some initial datum leads to a blow-up solution of the inter-critical defocusing nonlinear Schrödinger equation, there must exist an initial datum with the minimal -norm which will produce blow-up. Moreover, up to the invariant transformations, the set of such data is compact in . The main tool is the profile decomposition combined with the perturbation argument.
2010 MATHEMATICS SUBJECT CLASSIFICATION:
Acknowledgments
The authors would like to express their gratitude to the referees for useful comments.
Disclosure statement
No potential conflict of interest was reported by the authors.