On the global uniqueness of Stokes’ wave of extreme form
On the global uniqueness of Stokes’ wave of extreme form
复制标题
论斯托克斯波极端形式的全球独特性
DOI：
10.1093/imamat/hxq037
复制
发表时间：
2007
影响因子：
1.2
通讯作者：
Kenta Kobayashi
中科院分区：
文献类型：
--
作者：
Kenta Kobayashi
本文给出了极端形式Stokes波的全局唯一性的计算机辅助证明。极端形式的斯托克斯波是一种在波峰形成120度角的水波，被认为是内克拉索夫方程正解的极限，该方程表示自由表面上永久形式的周期重力波。数值验证方法在证明中起着重要的作用。关于极端形式的Stokes波的全局唯一性问题，不仅是一个长期悬而未决的问题，而且与一个重要的猜想--Stokes猜想有关。
We present a computer-assisted proof of the global uniqueness of Stokes' wave of extreme form. Stokes' wave of extreme form is a water wave which forms a corner of 120 degrees at the crest and is considered to be the limit of the positive solution of Nekrasov's equation which expresses periodic gravity waves of permanent form on the free surface. The numerical verification method plays an important role in the proof. As for the global uniqueness of Stokes' wave of extreme form, it is not only a longtime open problem but also is related to an important conjecture which is called Stokes' conjecture.