On the Well-Posedness and Scattering for the Gross–Pitaevskii Hierarchy via Quantum de Finetti

@article{Chen2014OnTW,
  title={On the Well-Posedness and Scattering for the Gross–Pitaevskii Hierarchy via Quantum de Finetti},
  author={T. Chen and C. Hainzl and N. Pavlovic and R. Seiringer},
  journal={Letters in Mathematical Physics},
  year={2014},
  volume={104},
  pages={871-891}
}
We prove the existence of scattering states for the defocusing cubic Gross–Pitaevskii (GP) hierarchy in $${\mathbb{R}^3}$$R3 . Moreover, we show that an exponential energy growth condition commonly used in the well-posedness theory of the GP hierarchy is, in a specific sense, necessary. In fact, we prove that without the latter, there exist initial data for the focusing cubic GP hierarchy for which instantaneous blowup occurs. 
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