The threshold for the focusing Gross–Pitaevskii equation with trapped dipolar quantum gases
The threshold for the focusing Gross–Pitaevskii equation with trapped dipolar quantum gases
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DOI：
10.1016/j.jmaa.2011.02.031
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发表时间：
2011-09
影响因子：
1.3
通讯作者：
Li Ma;Pei-sheng Cao
中科院分区：
文献类型：
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作者：
Li Ma;Pei-sheng Cao
本文讨论了描述捕获偶极量子气体的玻色-爱因斯坦凝聚的随时间聚焦的Gross-Pitaevskii方程解的整体存在阈值和有限时间爆破。通过构造新的交叉约束不变量集，根据对初始基准的适当假设，证明了相应的解要么全局存在，要么在有限时间内爆炸。
This paper concerns the threshold of global existence and finite time blow up of solutions to the time-dependent focusing Gross–Pitaevskii equation describing the Bose–Einstein condensation of trapped dipolar quantum gases. Via a construction of new cross-constrained invariant sets, it is shown that either the corresponding solution globally exists or blows up in finite time according to some appropriate assumptions about the initial datum.