论文标题
高度非线性浅水方程式在圆上的适合度
Well-posedness of a highly nonlinear shallow water equation on the circle
论文作者
论文摘要
我们介绍了在浅水波中的近期衍生模型方程的全面介绍和概述，并提供了对该方程所有可用研究的文献综述。此外，我们建立了一个新颖的结果，涉及相应的库奇问题的本地良好性，用于空间周期解决方案，并使用Sobolev Space $ h^s $的初始数据以$ s> 3/2 $的形式提供。
We present a comprehensive introduction and overview of a recently derived model equation for waves of large amplitude in the context of shallow water waves and provide a literature review of all the available studies on this equation. Furthermore, we establish a novel result concerning the local well-posedness of the corresponding Cauchy problem for space-periodic solutions with initial data from the Sobolev space $H^s$ on the circle for $s>3/2$.
