一类高阶Camassa-Holm型方程整体弱解的存在性

数学物理学报 ›› 2022, Vol. 42 ›› Issue (2): 427-441.

一类高阶Camassa-Holm型方程整体弱解的存在性

罗可欣^1,*(),赖绍永²

¹ 西华大学理学院成都 610039
² 西南财经大学数学学院成都 611130

收稿日期:2021-04-15 出版日期:2022-04-26 发布日期:2022-04-18
通讯作者: 罗可欣 E-mail:luokexin0122@163.com
基金资助:
国家自然科学基金(11471263);西华杯(2021190)

Global Weak Solutions to a High-Order Camass-Holm Type Equation

Kexin Luo^1,*(),Shaoyong Lai²

¹ School of Science, Xihua University, Chengdu 610039
² Department of Mathematics, Southwestern University of Finance and Economics, Chengdu 611130

Received:2021-04-15 Online:2022-04-26 Published:2022-04-18
Contact: Kexin Luo E-mail:luokexin0122@163.com
Supported by:
the NSFC(11471263);the Xihua Award(2021190)

摘要/Abstract

摘要：

使用粘性近似方法研究了一类高阶Camasa-Holm型方程. 推出了该类方程粘性解的高阶可积性估计及其空间导数的上界估计, 从而证明了该类方程整体弱解的存在性.

关键词: 整体弱解, 粘性近似, Camassa-Holm-type方程

Abstract:

The viscous approximation technique is employed to investigate the existence of global weak solutions for a high-order Camassa-Holm type equation. A higher integrability estimate of the viscous solutions for the equation and the upper bound estimate on the space derivative of its viscous solutions are derived to prove the existence.

Key words: Global weak solutions, Viscous approximations, Camassa-Holm-type equation

中图分类号:

O175.29

罗可欣,赖绍永. 一类高阶Camassa-Holm型方程整体弱解的存在性[J]. 数学物理学报, 2022, 42(2): 427-441.

Kexin Luo,Shaoyong Lai. Global Weak Solutions to a High-Order Camass-Holm Type Equation[J]. Acta mathematica scientia,Series A, 2022, 42(2): 427-441.

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