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Sharp Threshold of the Gross-Pitaevskii Equation with Trapped Dipolar Quantum Gases
  Published:2011-09-22
 Printed: Jun 2013
Canadian Mathematical Bulletin
  • Li Ma,
    Department of Mathematics, Henan Normal University, Xinxiang, 453007, China
  • Jing Wang,
    Department of Mathematics, Tsinghua University, Beijing, 100084, China
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Abstract

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 Gross-Pitaevskii equation, sharp threshold, global existence, blow up
MSC Classifications: 35Q55, 35A05, 81Q99 show english descriptions NLS-like equations (nonlinear Schrodinger) [See also 37K10]
General existence and uniqueness theorems
None of the above, but in this section 35Q55 - NLS-like equations (nonlinear Schrodinger) [See also 37K10]
35A05 - General existence and uniqueness theorems
81Q99 - None of the above, but in this section
 
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