Differential and Integral Equations

Parametric analyticity of functional variations of Dirichlet-Neumann operators

Carlo Fazioli and David P. Nicholls

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One of the important open questions in the theory of free--surface ideal fluid flows is the dynamic stability of traveling wave solutions. In a spectral stability analysis, the first variation of the governing Euler equations is required which raises both theoretical and numerical issues. With Zakharov and Craig and Sulem's formulation of the Euler equations in mind, this paper addresses the question of analyticity properties of first (and higher) variations of the Dirichlet--Neumann operator. This analysis will have consequences not only for theoretical investigations, but also for numerical simulations of spectral stability of traveling water waves.

Article information

Differential Integral Equations, Volume 21, Number 5-6 (2008), 541-574.

First available in Project Euclid: 20 December 2012

Permanent link to this document

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35Q35: PDEs in connection with fluid mechanics
Secondary: 35B35: Stability 35C07: Traveling wave solutions 35R35: Free boundary problems 76B07: Free-surface potential flows


Fazioli, Carlo; Nicholls, David P. Parametric analyticity of functional variations of Dirichlet-Neumann operators. Differential Integral Equations 21 (2008), no. 5-6, 541--574. https://projecteuclid.org/euclid.die/1356038632

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