最大振幅水波谱问题的负特征值
On negative eigenvalues of the spectral problem for water waves of highest amplitude
摘要：
我们考虑一个与旋转流的自由表面上的极端形式的定常水波有关的谱问题。证明了该问题的谱包含任意大的负特征值，且它们是简单的。此外，这种特征值的渐近性。
英文摘要：
We consider a spectral problem associated with steady water waves of extreme form on the free surface of a rotational flow. It is proved that the spectrum of this problem contains arbitrary large negative eigenvalues and they are simple. Moreover, the asymptotics of such eigenvalues is obtained.
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