Dynamical collapse of cylindrical symmetric dipolar Bose–Einstein condensates

Jacopo Bellazzini, Luigi Forcella

Research output: Contribution to journalArticlepeer-review

Abstract

We study the formation of singularities for cylindrical symmetric solutions to the Gross–Pitaevskii equation describing a dipolar Bose–Einstein condensate. We prove that solutions arising from initial data with energy below the energy of the Ground State and that do not scatter collapse in finite time. The main tools to prove our result are the variational characterization of the Ground State energy, suitable localized virial identities for cylindrical symmetric functions, and general integral and pointwise estimates for operators involving powers of the Riesz transform.

Original languageEnglish
Article number229
JournalCalculus of Variations and Partial Differential Equations
Volume60
Issue number6
Early online date19 Sep 2021
DOIs
Publication statusPublished - Dec 2021

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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