Dynamics of Solutions to the Gross–Pitaevskii Equation Describing Dipolar Bose–Einstein Condensates

Jacopo Bellazzini*, Luigi Forcella

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingChapter

1 Citation (Scopus)

Abstract

We review some recent results on the long-time dynamics of solutions to the Gross–Pitaevskii equation (GPE) governing non-trapped dipolar quantum gases. We describe the asymptotic behaviors of solutions for different initial configurations of the initial datum in the energy space, specifically for data below, above, and at the mass–energy threshold. We revisit some properties of powers of the Riesz transforms by means of the decay properties of the integral kernel associated to the parabolic biharmonic equation. These decay properties play a fundamental role in establishing the dynamical features of the solutions to the studied GPE.

Original languageEnglish
Title of host publicationQualitative Properties of Dispersive PDEs. INdAM 2021
PublisherSpringer
Pages25-57
Number of pages33
ISBN (Electronic)9789811964343
ISBN (Print)9789811964336
DOIs
Publication statusPublished - 30 Aug 2022

Publication series

NameSpringer INdAM Series
Volume52
ISSN (Print)2281-518X
ISSN (Electronic)2281-5198

ASJC Scopus subject areas

  • Mathematics(all)

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