Energy conservation and blowup of solutions for focusing Gross-Pitaevskii hierarchies

Thomas Chen, Nataša Pavlović, Nikolaos Tzirakis

Research output: Contribution to journalArticle

Abstract

We consider solutions of the focusing cubic and quintic Gross-Pitaevskii (GP) hierarchies. We identify an observable corresponding to the average energy per particle, and we prove that it is a conserved quantity. We prove that all solutions to the focusing GP hierarchy at the L2-critical or L 2-supercritical level blow up in finite time if the energy per particle in the initial condition is negative. Our results do not assume any factorization of the initial data.

Original languageEnglish (US)
Pages (from-to)1271-1290
Number of pages20
JournalAnnales de l'Institut Henri Poincare (C) Analyse Non Lineaire
Volume27
Issue number5
DOIs
StatePublished - Jan 1 2010

ASJC Scopus subject areas

  • Analysis
  • Mathematical Physics
  • Applied Mathematics

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