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.

引用

页数：31

共 50 条

[1] Growth of Sobolev norms for unbounded perturbations of the Schrodinger equation on flat tori
Bambusi, Dario
Langella, Beatrice
Montalto, Riccardo
JOURNAL OF DIFFERENTIAL EQUATIONS, 2022, 318 : 344 - 358
[2] Bounded Sobolev norms for linear Schrodinger equations under resonant perturbations
Wang, W. -M.
JOURNAL OF FUNCTIONAL ANALYSIS, 2008, 254 (11) : 2926 - 2946
[3] On the growth of Sobolev norms for Hartree equation
Shi, Qihong
Sun, Yuting
Saanouni, Tarek
JOURNAL OF EVOLUTION EQUATIONS, 2025, 25 (01)
[4] Unbounded Sobolev trajectories and modified scattering theory for a wave guide nonlinear Schrodinger equation
Xu, Haiyan
MATHEMATISCHE ZEITSCHRIFT, 2017, 286 (1-2) : 443 - 489
[5] Stability of linear KdV equation in a network with bounded and unbounded lengths
Parada, Hugo
Crepeau, Emmanuelle
Prieur, Christophe
2023 62ND IEEE CONFERENCE ON DECISION AND CONTROL, CDC, 2023, : 6199 - 6204
[6] Sobolev Stability of Plane Wave Solutions to the Nonlinear Schrodinger Equation
Wilson, Bobby
COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 2015, 40 (08) : 1521 - 1542
[7] Polynomial bounds on the Sobolev norms of the solutions of the nonlinear wave equation with time dependent potential
Vesselin Petkov
Nikolay Tzvetkov
Archiv der Mathematik, 2020, 114 : 71 - 84
[8] Polynomial bounds on the Sobolev norms of the solutions of the nonlinear wave equation with time dependent potential
Petkov, Vesselin
Tzvetkov, Nikolay
ARCHIV DER MATHEMATIK, 2020, 114 (01) : 71 - 84
[9] Unbounded Sobolev trajectories and modified scattering theory for a wave guide nonlinear Schrödinger equation
Haiyan Xu
Mathematische Zeitschrift, 2017, 286 : 443 - 489
[10] Reducibility of relativistic Schrodinger equation with unbounded perturbations
Sun, Yingte
Li, Jing
JOURNAL OF DIFFERENTIAL EQUATIONS, 2021, 286 : 215 - 247

← 1 2 3 4 5 →