没有稳定的小振幅水波支持的剪切流与静止的自由表面
No steady water waves of small amplitude are supported by a shear flow with still free surface
摘要：
本文考虑有限水深水面上具有涡量的定常重力波的二维自由边界问题。本文证明了自由面仍在坐标系中的水平剪切流不支持小振幅波，使得流动与时间无关，这种流动存在的涡量分布包括所有正的常数分布，以及具有任意正系数的线性和二次分布。
英文摘要：
The two-dimensional free-boundary problem describing steady gravity waves with vorticity on water of finite depth is considered. It is proved that no small-amplitude waves are supported by a horizontal shear flow whose free surface is still in a coordinate frame such that the flow is time-independent in it. The class of vorticity distributions for which such flows exist includes all positive constant distributions, as well as linear and quadric ones with arbitrary positive coefficients.
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