Abstract

In this note we discuss some recent results on extreme steady waves under gravity. They include the existence and regularity theorems for highest waves on finite depth with and without vorticity. Furthermore, we state new results concerning the asymptotic behavior of surface profiles near stagnation points. In particular, we find that the wave profile of an extreme wave is concave near each crest, provided that the vorticity is negative near the surface.

中文翻译：

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关于极限振幅的旋转波

摘要

在本说明中，我们讨论了重力作用下极端稳定波的一些最新结果。它们包括有限深度上有涡度和无涡度的最高波的存在性和规律性定理。此外，我们陈述了关于驻点附近表面轮廓的渐近行为的新结果。特别是，我们发现极端波的波形轮廓在每个波峰附近都是凹的，前提是表面附近的涡度为负。