Asymptotic behavior for nonlinear Schr?dinger equations with critical time-decaying harmonic potential
Asymptotic behavior for nonlinear Schr?dinger equations with critical time-decaying harmonic potential
复制标题
具有临界时间衰减谐波势的非线性薛定谔方程的渐近行为
DOI：
10.1016/j.jde.2021.09.028
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发表时间：
2021
影响因子：
2.4
通讯作者：
Kawamoto Masaki
中科院分区：
文献类型：
--
作者：
森岡 悠;Yoshiki Oshima;冨澤佑季乃;直江央寛;Suzuki Shintaro;Kawamoto Masaki
时间衰减谐振子产生弱衰减的色散估计，并在短程和长程之间改变非线性的阈值功率。在时间衰减谐振子的非临界情况下，这个阈值可以用多项式的非线性来表征。然而，在临界情况下，仅使用多项式项很难刻画阈值，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.