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

Abstract

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 [1], 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.

Keywords

• trapped quantum gases
• gross-pitaevskii equation
• blowup dynamics
• mass-energy threshold
• arbitrary large energy