Traveling two and three dimensional capillary gravity water waves
Traveling two and three dimensional capillary gravity water waves
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DOI：
10.1137/s0036141099354181
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发表时间：
2000-08-31
影响因子：
2
通讯作者：
Nicholls, DP
中科院分区：
文献类型：
--
作者：
Craig, W;Nicholls, DP
本文的主要结果是对于任何周期基本域，二维旅行重力波和毛细重力水波以及三维毛细重力水波的存在性定理。这是分叉理论中的一个问题，在二维情况下产生曲线，在三维情况下产生分叉表面。为了解决共振的存在，证明是基于变分公式和拓扑参数，这是与共振李雅普诺夫中心定理。
The main results of this paper are existence theorems for traveling gravity and capillary gravity water waves in two dimensions, and capillary gravity water waves in three dimensions, for any periodic fundamental domain. This is a problem in bifurcation theory, yielding curves in the two dimensional case and bifurcation surfaces in the three dimensional case. In order to address the presence of resonances, the proof is based on a variational formulation and a topological argument, which is related to the resonant Lyapunov center theorem.