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November  2020, 40(11): 6507-6527. doi: 10.3934/dcds.2020288

## Low regularity of solutions to the Rotation-Camassa-Holm type equation with the Coriolis effect

 College of Mathematical Sciences, Harbin Engineering University, Harbin, Heilongjiang 150001, China

* Corresponding author: Yanbing Yang

Received  April 2020 Revised  June 2020 Published  July 2020

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.

Citation: Runzhang Xu, Yanbing Yang. Low regularity of solutions to the Rotation-Camassa-Holm type equation with the Coriolis effect. Discrete & Continuous Dynamical Systems - A, 2020, 40 (11) : 6507-6527. doi: 10.3934/dcds.2020288
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