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Research Article | Open Access

Global weak solutions of nonlinear rotation-Camassa-Holm model

Zheng Dou1( ), Kexin Luo2
School of Economics, Xihua University, Chengdu 610039, China
School of Mathematics, Southwestern University of Finance and Economics, Chengdu 610030, China
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Abstract

A nonlinear rotation-Camassa-Holm equation, physically depicting the motion of equatorial water waves and having the Coriolis effect, is investigated. Using the viscous approximation tool, we obtain an upper bound estimate about the space derivative of the viscous solution and a high order integrable estimate about the time-space variables. Utilizing these two estimates, we prove that there exist H 1 ( R ) global weak solutions to the rotation-Camassa-Holm model.

Keywords

global weak solutionsexistencerotation-Camassa-Holm equation
CLC number: 35G25, 35L05

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AIMS Mathematics
Volume 8 Issue 7,
July 2023
Pages 15285-15298
DOI: 10.3934/math.2023781

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Cite this article:
Dou Z, Luo K. Global weak solutions of nonlinear rotation-Camassa-Holm model. AIMS Mathematics, 2023, 8(7): 15285-15298. https://doi.org/10.3934/math.2023781

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Received: 05 March 2023
Revised: 16 April 2023
Accepted: 23 April 2023
Published: 15 July 2023
©2023 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)