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

Published online by Cambridge University Press:  20 November 2018

Li Ma  and
Jing Wang
Li Ma
Affiliation:
Department of Mathematics, Henan Normal University, Xinxiang, 453007, China e-mail: [email protected]
Jing Wang
Affiliation:
Department of Mathematics, Tsinghua University, Beijing, 100084, China e-mail: [email protected]
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Abstract

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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

35Q5535A0581Q99Gross-Pitaevskii equationsharp thresholdglobal existenceblow-up
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 56 , Issue 2 , 01 June 2013 , pp. 378 - 387
Copyright
Copyright © Canadian Mathematical Society 2013

References

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