Studied herein is the local well-posedness of solutions with the low regularity in the periodic setting for a class of one-dimensional generalized Rotation-Camassa-Holm equation, which is considered as an asymptotic model to describe the propagation of shallow-water waves in the equatorial region with the weak Coriolis effect due to the Earth's rotation. With the aid of the semigroup approach and a refined viscosity technique, the local existence, uniqueness and continuity of periodic solutions in the spatial space $ C^1 $ is established based on the local structure of the dynamics along the characteristics.

中文翻译：

---

具有科里奥利效应的Rotation-Camassa-Holm型方程解的正则性低

本文研究了一类一维广义Rotation-Camassa-Holm方程在周期设置中具有低规则性的解的局部适定性，该方程被认为是描述浅水波在水中传播的渐近模型。由于地球自转，科里奥利效应较弱的赤道地区。借助半群方法和精细的黏度技术，基于动力学沿特征的局部结构，建立了空间空间$ C ^ 1 $中周期解的局部存在，唯一性和连续性。