On the well-posedness and scattering for the Gross-Pitaevskii hierarchy via quantum de Finetti Journal Article


Author(s): Chen, Thomas; Hainzl, Christian; Pavlović, Nataša; Seiringer, Robert
Article Title: On the well-posedness and scattering for the Gross-Pitaevskii hierarchy via quantum de Finetti
Alternate Title: Letters in Mathematical Physics
Affiliation IST Austria
Abstract: We prove the existence of scattering states for the defocusing cubic Gross-Pitaevskii (GP) hierarchy in ℝ3. Moreover, we show that an exponential energy growth condition commonly used in the well-posedness theory of the GP hierarchy is, in a specific sense, necessary. In fact, we prove that without the latter, there exist initial data for the focusing cubic GP hierarchy for which instantaneous blowup occurs.
Keywords: blowup; Gross-Pitaevskii hierarchy; ill-posedness; nonlinear Schrödinger equation; quantum de Finetti theorem; scattering
Journal Title: Letters in Mathematical Physics
Volume: 104
Issue 7
ISSN: 1573-0530
Publisher: Springer  
Date Published: 2014-05-07
Start Page: 871
End Page: 891
URL:
DOI: 10.1007/s11005-014-0693-2
Notes: The work of T.C. was supported by NSF grants DMS-1009448 and DMS-1151414 (CAREER). The work of N.P. was supported by NSF grant DMS-1101192. The work of R.S. was supported by NSERC.
Open access: yes (repository)
IST Austria Authors
  1. Robert Seiringer
    123 Seiringer
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