The Stokes conjecture for waves with vorticity
type: Item
instance of: scholarly article
title: The Stokes conjecture for waves with vorticity
zbMATH Open document ID: 1317.35209
published in: Annales de l'Institut Henri Poincaré. Analyse Non Linéaire
publication date: 2013-04-22T00:00:00Z
review text: Based on the author's abstract: Stagnation points of two-dimensional steady gravity free-surface water waves with vorticity are considered. The authors obtain for example that, in the case where the free surface is an injective curve, the asymptotics at any stagnation points is given either by the Stokes corner flow where the free surface has a corner of \(120\degree\), or the free surface ends in a horizontal cusp, or the free surface is horizontally flat at the stagnation point. The cusp case is a new feature in the case with vorticity, and it is not possible in the absence of vorticity. The authors exclude horizontally flat singularities in the case that the vorticity is 0 on the free surface. Here the vorticity may have infinitely many sign changes accumulating at the free surface, which makes this case particularly difficult and explains why it has been almost untouched by research so far.
Mathematics Subject Classification ID: 35Q35
Mathematics Subject Classification ID: 35R35
Mathematics Subject Classification ID: 76D07
zbMATH DE Number: 6156243
zbMATH Keywords: free surface
zbMATH Keywords: waves with vorticity
zbMATH Keywords: Stokes corner flow
Wikidata QID: Q122998761
author: Eugen Vărvărucă
author: Georg S. Weiss
MaRDI profile type: Publication
full work available at URL: j.anihpc.2012.05.001
OpenAlex ID: W2004888854
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DOI: 10.1016/J.ANIHPC.2012.05.001
description: scientific article; zbMATH DE number 6156243