Steady Periodic Capillary-Gravity Waves with Vorticity
Steady Periodic Capillary-Gravity Waves with Vorticity
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DOI：
10.1137/050630465
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发表时间：
2006-10
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影响因子：
--
通讯作者：
E. Wahlén
中科院分区：
文献类型：
--
作者：
E. Wahlén
本文证明了任意涡度分布的流动中存在稳态周期二维毛细管重力波。首先通过变量变换将原自由曲面问题转化为具有定域二阶拟线性边界条件的二阶拟线性椭圆方程；利用局部分岔理论，结合带有Venttsel边界条件的椭圆方程的Schauder理论和Pontryagin空间中的谱理论构造了这些方程的解。我们表明，一些分岔点是简单的，而另一些是双重的，这种情况已经知道发生在无旋转的毛细血管重力波的情况下。
In this paper we prove the existence of steady periodic two-dimensional capillary-gravity waves on flows with an arbitrary vorticity distribution. The original free-surface problem is first transformed to a second-order quasi-linear elliptic equation with a second-order quasi-linear boundary condition in a fixed domain by a change of variables. We then use local bifurcation theory combined with the Schauder theory of elliptic equations with Venttsel boundary conditions and spectral theory in Pontryagin spaces to construct the solutions. We show that some bifurcation points are simple while others are double, a situation already known to occur in the case of irrotational capillary-gravity waves.