Hostname: page-component-586b7cd67f-r5fsc Total loading time: 0 Render date: 2024-11-24T13:33:13.276Z Has data issue: false hasContentIssue false
  • English
  • Français

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 ([email protected])
Jian Zhang
Affiliation:
College of Mathematics and Software Science, Sichuan Normal University, Chengdu 610066, China ([email protected])
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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