CONTINUOUS DEPENDENCE ON DATA UNDER THE LIPSCHITZ METRIC FOR THE ROTATION-CAMASSA-HOLM EQUATION

doi:10.1007/s10473-021-0101-9

数学物理学报(英文版) ›› 2021, Vol. 41 ›› Issue (1): 1-18.doi: 10.1007/s10473-021-0101-9

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CONTINUOUS DEPENDENCE ON DATA UNDER THE LIPSCHITZ METRIC FOR THE ROTATION-CAMASSA-HOLM EQUATION

涂馨予¹, 穆春来², 邱蜀燕²

1. School of Mathematics and Statistics, Southwest University, Chongqing 400715, China;
2. College of Mathematics and Statistics, Chongqing University, Chongqing 401331, China

收稿日期:2020-02-03 修回日期:2020-08-28 出版日期:2021-02-25 发布日期:2021-04-06
通讯作者: Xinyu TU E-mail:xinyutu@cqu.edu.cn
作者简介:Chunlai MU,E-mail:clmu2005@163.com;Shuyan QIU E-mail:shuyanqiu0701@126.com
基金资助:
The first author was supported by Chongqing Post-doctoral Innovative Talent Support Progran, the Fundamental Research Funds for the Central Universities (XDJK2020C054), China Postdoctoral Science Foundation (2020M673102), the Natural Science Foundation of Chongqing, China, (cstc2020jcyj-bshX0071). The second author was supported by the Fundamental Research Funds for the Central Universities (2019CDJCYJ001, 2020CQJQ-Z001), the NSFC (11771062 and 11971082), Chongqing Key Laboratory of Analytic Mathematics and Applications.

CONTINUOUS DEPENDENCE ON DATA UNDER THE LIPSCHITZ METRIC FOR THE ROTATION-CAMASSA-HOLM EQUATION

Xinyu TU¹, Chunlai MU², Shuyan QIU²

1. School of Mathematics and Statistics, Southwest University, Chongqing 400715, China;
2. College of Mathematics and Statistics, Chongqing University, Chongqing 401331, China

Received:2020-02-03 Revised:2020-08-28 Online:2021-02-25 Published:2021-04-06
Contact: Xinyu TU E-mail:xinyutu@cqu.edu.cn
About author:Chunlai MU,E-mail:clmu2005@163.com;Shuyan QIU E-mail:shuyanqiu0701@126.com
Supported by:
The first author was supported by Chongqing Post-doctoral Innovative Talent Support Progran, the Fundamental Research Funds for the Central Universities (XDJK2020C054), China Postdoctoral Science Foundation (2020M673102), the Natural Science Foundation of Chongqing, China, (cstc2020jcyj-bshX0071). The second author was supported by the Fundamental Research Funds for the Central Universities (2019CDJCYJ001, 2020CQJQ-Z001), the NSFC (11771062 and 11971082), Chongqing Key Laboratory of Analytic Mathematics and Applications.

摘要/Abstract

摘要： In this article, we consider the Lipschitz metric of conservative weak solutions for the rotation-Camassa-Holm equation. Based on defining a Finsler-type norm on the tangent space for solutions, we first establish the Lipschitz metric for smooth solutions, then by proving the generic regularity result, we extend this metric to general weak solutions.

关键词: coriolis effect, rotation-Camassa-Holm equation, generic regularity, Lipschitz metric

Abstract: In this article, we consider the Lipschitz metric of conservative weak solutions for the rotation-Camassa-Holm equation. Based on defining a Finsler-type norm on the tangent space for solutions, we first establish the Lipschitz metric for smooth solutions, then by proving the generic regularity result, we extend this metric to general weak solutions.

Key words: coriolis effect, rotation-Camassa-Holm equation, generic regularity, Lipschitz metric

中图分类号:

35G25

涂馨予, 穆春来, 邱蜀燕. CONTINUOUS DEPENDENCE ON DATA UNDER THE LIPSCHITZ METRIC FOR THE ROTATION-CAMASSA-HOLM EQUATION[J]. 数学物理学报(英文版), 2021, 41(1): 1-18.

Xinyu TU, Chunlai MU, Shuyan QIU. CONTINUOUS DEPENDENCE ON DATA UNDER THE LIPSCHITZ METRIC FOR THE ROTATION-CAMASSA-HOLM EQUATION[J]. Acta mathematica scientia,Series B, 2021, 41(1): 1-18.

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CONTINUOUS DEPENDENCE ON DATA UNDER THE LIPSCHITZ METRIC FOR THE ROTATION-CAMASSA-HOLM EQUATION

CONTINUOUS DEPENDENCE ON DATA UNDER THE LIPSCHITZ METRIC FOR THE ROTATION-CAMASSA-HOLM EQUATION

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