In this paper, the Cauchy problem for the two layer viscous shallow water equations is investigated with third-order surface-tension terms and a low regularity assumption on the initial data. The global existence and uniqueness of the strong solution in a hybrid Besov space are proved by using the Littlewood-Paley decomposition and Friedrichs’ regularization method.

中文翻译：

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两层粘性浅水方程的柯西问题

在本文中，使用三阶表面张力项和对初始数据的低正则假设研究了两层粘性浅水方程的柯西问题。利用Littlewood-Paley分解和Friedrichs正则化方法证明了混合Besov空间强解的全局存在唯一性。