论文标题
表面变量中水波的弱公式
A Weak Formulation of Water Waves in Surface Variables
论文作者
论文摘要
在简短的说明中，我们在[AFM06]工作后得出了两个非局部方程的系统。具体而言，我们考虑具有一维自由表面的液体，用于与表面张力的无旋流流体。我们表明，这些方程对于在各个界面处的边界数据之间的直接图很有用，并考虑各种渐近方案。最后，对于周期性的行驶波解决方案，我们得出了一种新的单程方程式，该方程式是无衍生物的，并且有可能简化溶液中发现不催化膨胀的过程，并在求解计算时减少数值错误。
In this short note, we derive a system of two nonlocal equations for the water-wave problem following the work of [AFM06]. Specifically, we consider a fluid with a one-dimensional free surface for an irrotational fluid both with, and without, surface tension. We show that these equations can be useful for deriving direct maps between boundary data at the various interfaces and consider various asymptotic regimes. Finally, for periodic traveling wave solutions, we derive a new single-equation that is derivative free and has the potential to simplify the process of finding asymyptotic expansions of the solutions as well as reduce numerical errors when solving computationally.
