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

Thomas Chen, Christian Hainzl, Natasa Pavlovic, Robert Seiringer

Published 2013-11-09, updated 2014-03-27Version 2

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.