Global weak solutions of nonlinear rotation-Camassa-Holm model

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 integrabl...

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Bibliographic Details
Published inAIMS mathematics Vol. 8; no. 7; pp. 15285 - 15298
Main Authors Dou, Zheng, Luo, Kexin
Format Journal Article
LanguageEnglish
Published AIMS Press 01.01.2023
Subjects
existence
global weak solutions
rotation-camassa-holm equation
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ISSN2473-6988
2473-6988
DOI10.3934/math.2023781

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Summary: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(\mathbb{R}) $ global weak solutions to the rotation-Camassa-Holm model.
ISSN:2473-6988
2473-6988
DOI:10.3934/math.2023781