Author(s):

Chen, Thomas; Hainzl, Christian; Pavlović, Nataša; Seiringer, Robert

Article Title: 
On the wellposedness and scattering for the GrossPitaevskii 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 GrossPitaevskii (GP) hierarchy in ℝ3. Moreover, we show that an exponential energy growth condition commonly used in the wellposedness 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; GrossPitaevskii hierarchy; illposedness; nonlinear Schrödinger equation; quantum de Finetti theorem; scattering

Journal Title:

Letters in Mathematical Physics

Volume: 
104

Issue 
7

ISSN:

15730530

Publisher:

Springer

Date Published:

20140507

Start Page: 
871

End Page:

891

URL: 

DOI: 
10.1007/s1100501406932

Notes: 
The work of T.C. was supported by NSF grants DMS1009448 and DMS1151414 (CAREER). The work of N.P. was supported by NSF grant DMS1101192. The work of R.S. was supported by NSERC.

Open access: 
yes (repository) 