1. CMB 2011 (vol 56 pp. 378)
|Sharp Threshold of the Gross-Pitaevskii Equation with Trapped Dipolar Quantum Gases|
In this paper, we consider the Gross-Pitaevskii equation for the trapped dipolar quantum gases. We obtain the sharp criterion for the global existence and finite time blow up in the unstable regime by constructing a variational problem and the so-called invariant manifold of the evolution flow.
Keywords:Gross-Pitaevskii equation, sharp threshold, global existence, blow up
Categories:35Q55, 35A05, 81Q99