Going beyond the threshold: Blowup criteria with arbitrary large energy in trapped quantum gases

Abstract

<abstract><p>The present paper considers the blowup properties in trapped dipolar quantum gases modelled by the Gross-Pitaevskii equation. More precisely, through analyzing the temporal evolution of $ J'(t) $ in the form of uncertain principle <sup>[<xref ref-type="bibr" rid="b1">1</xref>]</sup>, we provide some invariant evolution flows. Based on that, we establish the global existence versus blowup dichotomy of solutions above the mass-energy threshold. Meanwhile, we can estimate the behaviour of solutions with arbitrary large energy.</p></abstract>