Under consideration in the present paper is a mathematical model proposed as an equation of long-crested shallow-water waves propagating in one direction with the effect of Earth’s rotation. The system is called Rotation-Camassa-Holm system (RCH2). The local well-posedness of the periodic Cauchy problem is then established by the linear transport theory. Then, wave-breaking phenomena is investigated based on the method of characteristics and the Riccati-type differential inequality with two different kinds of methods. Finally, the wave-breaking data are illustrated and the existence of global solutions is obtained in detail for the periodic RCH2 system.

中文翻译：

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非局部周期Rotation-Camassa-Holm系统的爆炸现象和整体存在

本文考虑的是一个数学模型，它是由地球自转作用在一个方向传播的长波浅水波方程式。该系统称为Rotation-Camassa-Holm系统（RCH2）。然后通过线性输运理论建立了周期性柯西问题的局部适定性。然后，根据特征方法和Riccati型微分不等式，采用两种不同的方法研究了破波现象。最后，说明了破波数据，并详细了解了周期性RCH2系统的整体解的存在。