非线性Schrodinger方程长时间稳定性的一个估计

An estimation of long time stability of the nonlinear Schrodinger equation

摘要:

本文考虑了一维环面上的非线性 Schrodinger 方程小振幅解的稳定性. 在正则指标s大于0.5小于1的条件下, 本文给出了方程小振幅解的长时间稳定性的一个估计.

Abstract:

In this paper, we consider the long time stability of the small amplitude solutions of the nonlinear Schrodinger equation. Under the regularity index s fullfilling 1/2 < s < 1, we give an estimation for the long time stability of the small amplitude solutions with initial data of size ε, where ε is postive and suffciently small.