论文标题
线性波方程的Sobolev规范的稳定性具有无限的扰动
The stability of Sobolev norms for the linear wave equation with unbounded perturbations
论文作者
论文摘要
在本文中，我们证明了线性波方程解决方案的Sobolev规范，其秩序的扰动无限驱动一直存在。主要证明是基于线性波方程的KAM降低性。据我们所知，这是线性波方程的第一个降低性结果，在圆环上具有一般的准周期无限势。
In this paper, we prove that the Sobolev norm of solutions of the linear wave equation with unbounded perturbations of order one stay bounded for the all time. The main proof is based on the KAM reducibility of the linear wave equation. To the best of our knowledge, this is the first reducibility result of the linear wave equation with general quasi-periodic unbounded potentials on the torus.
