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

Chen, Thomas; Pavlović, Nataša

doi:10.1090/S0002-9939-2012-11308-5

A new proof of existence of solutions for focusing and defocusing Gross-Pitaevskii hierarchies
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by Thomas Chen and Nataša Pavlović PDF

Proc. Amer. Math. Soc. 141 (2013), 279-293 Request permission

Abstract:

We consider the cubic and quintic Gross-Pitaevskii (GP) hierarchies in $d\geq 1$ 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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