论文标题
非线性schrödinger方程的渐近行为，具有关键的时间偿还谐波电位
Asymptotic behavior for nonlinear Schrödinger equations with critical time-decaying harmonic potential
论文作者
论文摘要
时间付费的谐波振荡器会产生衰减较弱的分散估计，并改变短距离和远距离之间的非线性阈值能力。在时间偿还谐波振荡器的非关键情况下，该阈值可以以多项式非线性为特征。但是，在关键情况下，很难仅使用多项式项来表征阈值，因此我们使用对数非线性项。
Time-decaying harmonic oscillators yield dispersive estimates with weak decay, and change the threshold power of the nonlinearity between the short and the long range. In the non-critical case for the time-decaying harmonic oscillator, this threshold can be characterized by polynomial nonlinearities. However, in the critical case, it is difficult to characterize the threshold using only polynomial terms, and thus we use logarithmic nonlinear terms.
