The threshold for the focusing Gross-Pitaevskii equation with trapped dipolar quantum gases |
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| Authors: | Li Ma Pei Cao |
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| Institution: | a Department of Mathematics, Henan Normal University, Xinxiang 453007, China
b Department of Mathematical Sciences, Tsinghua University, Beijing 100084, China |
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| Abstract: | 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. |
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| Keywords: | Threshold Global existence Blow up Gross-Pitaevskii equation |
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