论文标题
稳定周期性水波的全局分叉结构和几何特性
Global bifurcation structure and geometric properties for steady periodic water waves with vorticity
论文作者
论文摘要
本文研究了欧拉方程描述的经典水波问题，其在平坦底部的重力影响下具有自由表面。基于基本工作\ cite {constantInstrauss}，我们首先获得了两条连续分叉曲线，它们仅使用修改的分析分叉定理仅一次满足层流。它们是对称波，其轮廓在每个峰顶和槽之间都是单调的。此外，我们发现连续的顶峰和槽之间的波轮廓至少有一个拐点，并且自由表面在任何波峰上都严格凹入，并且在任何槽中都严格凸出。此外，为了呈良好的涡度，我们证明了水波的垂直位移随深度降低。
This paper studies the classical water wave problem with vorticity described by the Euler equations with a free surface under the influence of gravity over a flat bottom. Based on fundamental work \cite{ConstantinStrauss}, we first obtain two continuous bifurcation curves which meet the laminar flow only one time by using modified analytic bifurcation theorem. They are symmetric waves whose profiles are monotone between each crest and trough. Furthermore, we find that there is at least one inflection point on the wave profile between successive crests and troughs and the free surface is strictly concave at any crest and strictly convex at any trough. In addition, for favorable vorticity, we prove that the vertical displacement of water waves decreases with depth.
