论文标题
关于非线性schrödinger方程的衰减属性
On decaying properties of nonlinear Schrödinger equations
论文作者
论文摘要
在本文中，我们讨论了使用各种初始数据（确定性和随机数据）的非线性schrödinger方程的3D立方偏置的溶液的定量（点状）衰减估计值。我们表明，非线性溶液享有与线性溶液相同的衰减速率。对初始数据的规律性假设远低于以前的结果（请参阅\ cite {fan2021decay}及其中的参考文献），此外，我们量化了衰减，这是这项工作的另一个新颖性。此外，我们表明，初始数据的（物理）随机化可用于替换$ l^1 $ -DATA假设（有关$ l^1 $ -DATA假设的必要性，请参见\ cite {fan2022note}。最后，我们注意到此方法也可以应用于其他非线性分散方程的衰减估计值。
In this paper we discuss quantitative (pointwise) decay estimates for solutions to the 3D cubic defocusing Nonlinear Schrödinger equation with various initial data, deterministic and random. We show that nonlinear solutions enjoy the same decay rate as the linear ones. The regularity assumption on the initial data is much lower than in previous results (see \cite{fan2021decay} and the references therein) and moreover we quantify the decay, which is another novelty of this work. Furthermore, we show that the (physical) randomization of the initial data can be used to replace the $L^1$-data assumption (see \cite{fan2022note} for the necessity of the $L^1$-data assumption). At last, we note that this method can be also applied to derive decay estimates for other nonlinear dispersive equations.
