论文标题
Euler方程的空间准周期溶液
Spatially quasi-periodic solutions of the Euler equation
论文作者
论文摘要
我们开发了一个框架，用于研究$ \ mathbb {r}^n $上的准周期地图和差异性。作为一个应用程序，我们证明了Euler方程在$ \ mathbb {r}^n $上局部很好地摆放在准周期矢量字段的空间中。特别是，该方程保留了初始数据的空间准周期性。证明了解决方案对时间和初始数据的分析依赖性的几个结果。
We develop a framework for studying quasi-periodic maps and diffeomorphisms on $\mathbb{R}^n$. As an application, we prove that the Euler equation is locally well posed in a space of quasi-periodic vector fields on $\mathbb{R}^n$. In particular, the equation preserves the spatial quasi-periodicity of the initial data. Several results on the analytic dependence of solutions on the time and the initial data are proved.
