In this article, we consider the Lipschitz metric of conservative weak solutions for the rotation-Camassa-Holm equation. Based on defining a Finsler-type norm on the tangent space for solutions, we first establish the Lipschitz metric for smooth solutions, then by proving the generic regularity result, we extend this metric to general weak solutions.

中文翻译：

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旋转-Camassa-Holm 方程在 Lipschitz 度量下对数据的连续依赖

在本文中，我们考虑旋转-Camassa-Holm 方程的保守弱解的 Lipschitz 度量。基于在解的切空间上定义 Finsler 型范数，我们首先建立平滑解的 Lipschitz 度量，然后通过证明通用正则性结果，我们将该度量扩展到一般弱解。