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≥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, klma, and used in our earlier work, chpa2.
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