| 张健,李晓光.带调和势的临界非线性Schr(o)dinger方程的爆破解[J].数学年刊A辑,2009,30(5):587~596 |
| 带调和势的临界非线性Schr(o)dinger方程的爆破解 |
| Blow-Up Solutions for Critical Nonlinear Schr(o)dinger Equation with Harmonic Potential |
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| DOI： |
| 中文关键词: 非线性Schr(o)dinger方程 吸引Bose-Einstein凝聚 爆破率 L2-集中 |
| 英文关键词:Nonlinear Schr¨odinger equation, Attractive Bose-Einstein
condensates, Blow-up rate, L2-concentration |
| 基金项目:国家自然科学基金(No.10771151)资助的项目 |
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| 中文摘要: |
| 讨论了带调和势的临界非线性Schr(o)dinger方程的Cauchy问题,它是描述著名的Bose-Einstein凝聚的模型.得到带调和势的临界非线性Schr(o)diager方程爆破解的爆破速率的下界估计.进而,还得到径向对称爆破解的L2-集中性质. |
| 英文摘要: |
| The authors consider the blow-up solutions of the Cauchy problem for the critical
nonlinear Schr¨odinger equation with a harmonic potential, which models the attractive
Bose-Einstein condensate. The lower bound of blow-up rate is obtained. Furthermore, the
L2-concentration property of the radially symmetric blow-up solutions is obtained. |
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