Sharp Threshold of the Gross-Pitaevskii Equation with Trapped Dipolar Quantum Gases

Canadian mathematical bulletin

Li Ma¹  Jing Wang² 

[1] Department of Mathematics, Henan Normal University, Xinxiang, 453007, China;Department of Mathematics, Tsinghua University, Beijing, 100084, China

关键词: Gross-Pitaevskii equation;    sharp threshold;    global existence;    blow up;   

DOI  :  10.4153/CMB-2011-181-2

学科分类：数学（综合）

来源: University of Toronto Press * Journals Division

【 摘 要 】

In this paper, we consider the Gross-Pitaevskii equation for thetrapped dipolar quantum gases. We obtain the sharp criterion for theglobal existence and finite time blow up in the unstable regime byconstructing a variational problem and the so-called invariantmanifold of the evolution flow.

【 授权许可】

Unknown