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We consider the cubic and quintic Gross-Pitaevskii (GP) hierarchies in d≥ 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 and used in our earlier work.
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Chen et al. (2012) studied this question.
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