A new proof of existence of solutions for focusing and defocusing Gross-Pitaevskii hierarchies

Abstract

We consider the cubic and quintic Gross-Pitaevskii (GP) hierarchies in $d\ge 1$ dimensions, for focusing and defocusing interactions. We present a new proof of existence of solutions that does not require the a priori bound on the spacetime norm, which was introduced in the work of Klainerman and Machedon, \cite{klma}, and used in our earlier work, \cite{chpa2}.

AMS Latex, 14 pages. Title changed, major revision. This preprint replaces a previous version which contained an error in Proposition 4.1 that was pointed out to us by I. Rodnianski

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