论文标题
分析框架中水浪系统的凯奇理论
Cauchy theory for the water waves system in an analytic framework
论文作者
论文摘要
在本文中，我们考虑了在平坦的底部和任意空间维度的域中，重力水波的问题。我们证明，如果数据在分析功能的空间中具有$ \ varepsilon $，这些功能的大小$σ$中具有全体形态扩展，则该解决方案的尺寸最高为$ c/\ varepsilon $在分析功能的空间中，该空间具有$ t $ t $ holomorphic Extensive y sip $ size $ nive $ s $ c的$ c'fime t $ t $ t $。
In this paper we consider the Cauchy problem for gravity water waves, in a domain with a flat bottom and in arbitrary space dimension. We prove that if the data are of size $\varepsilon$ in a space of analytic functions which have a holomorphic extension in a strip of size $σ$, then the solution exists up to a time of size $C/\varepsilon$ in a space of analytic functions having at time $t$ a holomorphic extension in a strip of size $σ- C'\varepsilon t$.
