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THRESHOLD OF GLOBAL EXISTENCE FOR THE CRITICAL NONLINEAR GROSS–PITAEVSKII EQUATION

Published online by Cambridge University Press:  09 February 2007

Guanggan Chen  and
Jian Zhang
Guanggan Chen
Affiliation:
College of Mathematics and Software Science, Sichuan Normal University, Chengdu 610066, China (chenguanggan@hotmail.com)
Jian Zhang
Affiliation:
College of Mathematics and Software Science, Sichuan Normal University, Chengdu 610066, China (chenguanggan@hotmail.com)
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Abstract

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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 $p=1+(4/N)$?

Keywords

Primary 35Q5535B3535A15thresholdglobal existenceblow-upcriticalGross–Pitaevskii equation
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