论文标题
关于对称和稳定连续分层周期水波的恢复
On symmetry and recovery of steady continuous stratified periodic water waves
论文作者
论文摘要
本文考虑了二维稳定的连续分层周期性水波。首先，我们证明，当它通过利用最大原理和表面剖面的分析来严格单调时，就必须对波峰线进行对称。然后，在统一的倾斜导数问题上利用标准的Schauder估计值，以表明所有流线都是真实的分析（包括自由表面）。基于上述对称性和流线的规律性，我们最终提供了一种分析扩展方法，以从对称性和波高度轴上从水平速度中恢复水波。最值得注意的是，这里的所有结果不仅适用于小振幅，而且适合大幅度。
This paper considers two-dimensional steady continuous stratified periodic water waves. Firstly, we prove that each streamline must be symmetric about the crest line when it is strictly monotonous between troughs and crests by exploiting the maximum principle and analysis of surface profile. Then, standard Schauder estimates are exploited on the uniform oblique derivative problems to show that all streamlines are real analytic (including the free surface). Based on above symmetry and regularity of streamlines, finally we provide an analytic expansion method to recover the water waves from horizontal velocity on the axis of symmetry and wave height. Most notably, all of results here are suitable not only for small amplitude but also for large amplitude.
