THRESHOLD OF GLOBAL EXISTENCE FOR THE CRITICAL NONLINEAR GROSS–PITAEVSKII EQUATION
2007 ◽
Vol 50
(1)
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pp. 63-71
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AbstractThis paper is concerned with the critical nonlinear Gross–Pitaevskii equation, which describes the attractive Bose–Einstein condensate under a magnetic trap. We derive a sharp threshold between the global existence and the blowing-up of the system. Furthermore, we answer the question: how small are the initial data, such that the system has global solutions for the nonlinear critical power $p=1+(4/N)$?
2013 ◽
Vol 27
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pp. 1350184
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2010 ◽
Vol 24
(30)
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pp. 2911-2920
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1999 ◽
Vol 261
(5-6)
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pp. 337-344
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2008 ◽
Vol 17
(10)
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pp. 2150-2154
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1999 ◽
Vol 68
(12)
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pp. 3840-3847
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1996 ◽
Vol 77
(6)
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pp. 988-991
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