An estimate for the Morse index of a Stokes wave

Eugene Shargorodsky

doi:10.1007/s00205-013-0614-z

An estimate for the Morse index of a Stokes wave

Eugene Shargorodsky^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

9 Citations (Scopus)

Abstract

Stokes waves are steady periodic water waves on the free surface of an infinitely deep irrotational two dimensional flow under gravity without surface tension. They can be described in terms of solutions of the Euler-Lagrange equation of a certain functional. This allows one to define the Morse index of a Stokes wave. It is well known that if the Morse indices of the elements of a set of non-singular Stokes waves are bounded, then none of them is close to a singular one. The paper presents a quantitative variant of this result.

Original language	English
Pages (from-to)	41-59
Number of pages	19
Journal	ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS
Volume	209
Issue number	1
Early online date	29 Mar 2013
DOIs	https://doi.org/10.1007/s00205-013-0614-z
Publication status	Published - Jul 2013

Keywords

math.SP
math.AP

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An estimate for the Morse index of a Stokes wave

Abstract

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