The bifurcation of interfacial capillary-gravity waves under \(\text{O}(2)\) symmetry
type: Item
instance of: scholarly article
title: The bifurcation of interfacial capillary-gravity waves under \(\text{O}(2)\) symmetry
zbMATH Open document ID: 1238.37033
published in: Communications on Pure and Applied Analysis
publication date: 2011-12-19T00:00:00Z
review text: The uniform steady stratified laminar motion of two ideal fluids with different densities in a layer parallel to their interface is considered. The problem of determination of small disturbances that arise on the interface of two fluids is reduced to the system of two nonlinear integro-differential equations (IDEs) with respect to two unknown functions \(\Theta\) and \(S\) parameterizing the interface and depending on three parameters (speed of upper and lower fluid and capillarity at the interface). The disturbance waves of small amplitude arise at the nonlinear interaction between two higher harmonics in the linearization. In two appropriate Banach spaces the system of IDEs is solved by bifurcation theory methods and \(\text{O}(2)\)-symmetry representation conditions.
reviewed by: Irina V. Konopleva
Mathematics Subject Classification ID: 37N10
Mathematics Subject Classification ID: 37G40
Mathematics Subject Classification ID: 76B15
Mathematics Subject Classification ID: 35Q30
zbMATH DE Number: 5989656
zbMATH Keywords: bifurcation
zbMATH Keywords: fluid-fluid interface
zbMATH Keywords: Lyapunov-Schmidt
zbMATH Keywords: group invariance
author: Mark C. W. Jones
MaRDI profile type: Publication
full work available at URL: cpaa.2011.10.1183
OpenAlex ID: W1978035925
DOI: 10.3934/CPAA.2011.10.1183
description: scientific article; zbMATH DE number 5989656