On the well-posedness and scattering for the Gross-Pitaevskii hierarchy via quantum de Finetti

Authors
Type
Published Article
Publication Date
Mar 27, 2014
Submission Date
Nov 09, 2013
Identifiers
DOI: 10.1007/s11005-014-0693-2
Source
arXiv
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Abstract

We prove the existence of scattering states for the defocusing cubic Gross-Pitaevskii (GP) hierarchy in \${\mathbb R}^3\$. Moreover, we show that an 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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