Convexity of Stokes waves of extreme form
type: Item
instance of: scholarly article
title: Convexity of Stokes waves of extreme form
zbMATH Open document ID: 1064.76017
author: P. I. Plotnikov
author: John F. Toland
published in: Archive for Rational Mechanics and Analysis
publication date: 2004-09-22T00:00:00Z
review text: The authors establish existence of a periodic Stokes waves of extreme form which has a convex profile between consecutive stagnation points where there is a corner with contact angle of \(120^\circ\). The methods reduce the problem first to finding a holomorphic function with simultaneously prescribed Dirichlet and Neumann boundary conditions on a piecewise-convex, periodic, planar curve. The problem is then rewritten as an integral equation, following Nekrasov's theory. Finally, the integral equation is homotoped to a simpler form, where existence of a convex solution is explicitly known. The major difficulty lies in preserving convexity during the homotopy.
reviewed by: Arnd Scheel
Mathematics Subject Classification ID: 76B15
Mathematics Subject Classification ID: 35Q35
zbMATH DE Number: 2102299
zbMATH Keywords: homotopy method
zbMATH Keywords: existence
zbMATH Keywords: holomorphic function
MaRDI profile type: Publication
full work available at URL: s00205-003-0292-3
OpenAlex ID: W2035784707
DOI: 10.1007/S00205-003-0292-3
description: scientific article; zbMATH DE number 2102299