A new blow-up criterion for Gross-Pitaevskii equation

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• 作者：Zhongtao Yue ; ^{zhongtaoyue920601@163.com" class="auth_mail" title="E-mail the corresponding author} ; Xiaoguang Li ; Jian Zhang
• 关键词：Gross&ndash ; Pitaevskii equation ; Invariant set ; Blow-up
• 刊名：Applied Mathematics Letters
• 出版年：2016
• 出版时间：December 2016
• 年：2016
• 卷：62
• 期：Complete
• 页码：16-22
• 全文大小：616 K

文摘

This paper is devoted to the study of the Gross–Pitaevskii equation, which describes the attractive Bose–Einstein condensate under a magnetic trap. By establishing an invariant set and applying the Gagliardo–Nirenberg type inequality, we then get the existence of blow-up solutions with arbitrary large initial energy.