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

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Type
Published Article
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Submission Date
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DOI: 10.1007/s11005-014-0693-2
Source
arXiv
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Yellow
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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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