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.
Keywords
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}
}