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


Authors: Thomas Chen and Nataša Pavlović
Journal: Proc. Amer. Math. Soc. 141 (2013), 279-293
MSC (2010): Primary 35Q55
DOI: https://doi.org/10.1090/S0002-9939-2012-11308-5
Published electronically: May 18, 2012
MathSciNet review: 2988730
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Abstract | References | Similar Articles | Additional Information

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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Additional Information

Thomas Chen
Affiliation: Department of Mathematics, University of Texas at Austin, Austin, Texas 78712
Email: tc@math.utexas.edu

Nataša Pavlović
Affiliation: Department of Mathematics, University of Texas at Austin, Austin, Texas 78712
Email: natasa@math.utexas.edu

DOI: https://doi.org/10.1090/S0002-9939-2012-11308-5
Received by editor(s): December 22, 2010
Received by editor(s) in revised form: June 17, 2011
Published electronically: May 18, 2012
Communicated by: Hart F. Smith
Article copyright: © Copyright 2012 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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