Global weak solutions of nonlinear rotation-Camassa-Holm model

Zheng Dou; Kexin Luo; Zheng Dou; Kexin Luo

doi:10.3934/math.2023781

AIMS Mathematics

2023, Volume 8, Issue 7: 15285-15298. doi: 10.3934/math.2023781

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Research article

Global weak solutions of nonlinear rotation-Camassa-Holm model

Zheng Dou ^{1
,
,},
Kexin Luo ²

1.
School of Economics, Xihua University, Chengdu 610039, China
2.
School of Mathematics, Southwestern University of Finance and Economics, Chengdu 610030, China

Received: 05 March 2023 Revised: 16 April 2023 Accepted: 23 April 2023 Published: 25 April 2023
MSC : 35G25, 35L05

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.
- global weak solutions,
- existence,
- rotation-Camassa-Holm equation
Citation: Zheng Dou, Kexin Luo. Global weak solutions of nonlinear rotation-Camassa-Holm model[J]. AIMS Mathematics, 2023, 8(7): 15285-15298. doi: 10.3934/math.2023781

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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(\mathbb{R}) $ global weak solutions to the rotation-Camassa-Holm model.

References

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