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THRESHOLD OF GLOBAL EXISTENCE FOR THE CRITICAL NONLINEAR GROSS–PITAEVSKII EQUATION
Published online by Cambridge University Press: 09 February 2007
Abstract
This 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 $p=1+(4/N)$?
- Type
- Research Article
- Information
- Proceedings of the Edinburgh Mathematical Society , Volume 50 , Issue 1 , February 2007 , pp. 63 - 71
- Copyright
- Copyright © Edinburgh Mathematical Society 2007
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