The stability of Sobolev norms for the linear wave equation with unbounded perturbations

被引：2
|
作者：
Sun, Yingte [1 ]
机构：
[1] Yangzhou Univ, Sch Math Sci, Yangzhou, Peoples R China
来源：
JOURNAL OF MATHEMATICAL PHYSICS | 2023年 / 64卷 / 12期
基金：
中国国家自然科学基金;
关键词：
QUASI-PERIODIC SOLUTIONS; SCHRODINGER-EQUATIONS; REDUCIBILITY; KAM; GROWTH; OSCILLATOR; DISCRETE; SPECTRUM;
D O I：
10.1063/5.0157908
中图分类号：
O4 [物理学];
学科分类号：
0702 ;
摘要：
In this paper, we prove that the Sobolev norms of solutions for the linear wave equation with unbounded perturbations of order one remain bounded for 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 for the linear wave equation with general quasi-periodic unbounded perturbations on the one-dimensional torus.
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页数：31
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