Electron. J. Differential Equations, Vol. 2018 (2018), No. 78, pp. 1-23.

Blow-up of solutions to the rotation b-family system modeling equatorial water waves

Min Zhu, Ying Wang

We consider the blow-up mechanism to the periodic generalized rotation b-family system (R-b-family system). This model can be derived from the f-plane governing equations for the geographical water waves with a constant underlying current in the equatorial water waves with effect of the Coriolis force. When b=2, it is a rotation two-component Camassa-Holm (R2CH) system. We consider the periodic R2CH system when linear dispersion is absent (which model is called r2CH system) and derive two finite-time blow-up results.

Submitted December 4, 2017. Published March 20, 2018.
Math Subject Classifications: 35B44, 35G25.
Key Words: Rotation b-family system; blow up; wave-breaking.

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Min Zhu
Department of Mathematics
Nanjing Forestry University
Nanjing, 210037, China
email: zhumin@njfu.edu.cn
  Ying Wang
Department of Mathematics
University of Electronic Science and Technology of China
Chengdu 611731, China
email: nadine_1979@163.com

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