带调和势的超临界非线性Schrdinger方程的最佳门槛  

Sharper Thresholds in Supercritical Nonlinear Schrdinger Equation with a Harmonic Potential

作　　者：张健[1] 陈光淦[1] 

机构地区：[1]四川师范大学数学与软件科学学院,成都610066

出　　处：《数学学报（中文版）》2007年第6期1381-1390,共10页Acta Mathematica Sinica：Chinese Series

基　　金：四川省教育厅重点科研项目(2006A063);四川省科技厅应用基础科研项目(07JY029-012);四川师范大学博士科研启动基金资助

摘　　要：考虑带调和势的超临界非线性Schrdinger方程,解决了该方程整体解和爆破解存在所依赖的初始条件的最佳分界门槛.通过构造两类强制变分问题和建立局部不变半流,运用势井方法和凹方法,获得了该方程在两个不同的空间中的整体解和爆破解的最佳门槛条件.We investigate the sharper threshold phenomena associated with the non- linear SchrSdinger equation with a harmonic potential, where the answer to questions of global existence vs. finite time blowup depends on the initial data. By constructing two types of constrained variational problems and establishing the invariant local semi-flows, we derive two different thresholds of blowup and global existence for the supercritical case of the system in two different spaces by applying the potential well argument and the concavity method.

关 键 词：吸引Bose-Einstein凝聚 非线性SCHROEDINGER方程 最佳门槛 整体存在 

分 类 号：O175.24[理学—数学]