On the Cauchy problem of 3-D energy-critical Schrödinger equations with subcritical perturbations
On the Cauchy problem of 3-D energy-critical Schrödinger equations with subcritical perturbations
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DOI：
10.1016/j.jde.2006.08.010
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发表时间：
2006-11
影响因子：
2.4
通讯作者：
Xiaoyi Zhang
中科院分区：
文献类型：
--
作者：
Xiaoyi Zhang
研究了具有能量临界的三维五次非线性薛定谔方程在次临界非线性扰动λ1下的整体适定性、散射和爆破现象|u| PU.我们发现当五次项是散焦的时，无论λ 1的符号是什么，解总是整体的.散射会在扰动散焦且43<p<4时发生，或者当溶液的质量足够小且43 p<4时发生。当五次项聚焦时，我们给出了某些解的爆破。
We investigate the global well-posedness, scattering and blow up phenomena when the 3-D quintic nonlinear Schrödinger equation, which is energy-critical, is perturbed by a subcritical nonlinearity λ1|u|pu. We find when the quintic term is defocussing, then the solution is always global no matter what the sign of λ1is. Scattering will occur either when the perturbation is defocussing and 43<p<4 or when the mass of the solution is small enough and 43⩽p<4. When the quintic term is focusing, we show the blow up for certain solutions.