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On negative eigenvalues of the spectral problem for water waves of highest amplitude

Analysis of PDEs 2021-08-10 v2 Mathematical Physics math.MP Spectral Theory

Abstract

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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Cite

@article{arxiv.2104.04723,
  title  = {On negative eigenvalues of the spectral problem for water waves of highest amplitude},
  author = {Vladimir Kozlov and Evgeniy Lokharu},
  journal= {arXiv preprint arXiv:2104.04723},
  year   = {2021}
}