Bifurcation and stability of cellular states in magnetic fluids
type: Item
instance of: scholarly article
title: Bifurcation and stability of cellular states in magnetic fluids
zbMATH Open document ID: 0594.76106
DOI: 10.4171/ZAA/163
author: K. Beyer
published in: Zeitschrift für Analysis und ihre Anwendungen
publication date: 1985-01-01T00:00:00Z
review text: This paper continues earlier work of the author [Z. Angew. Math. Mekh. 60, 235-240 (1980; Zbl 0462.76044) and Z. Anal. Anwend. 2, 385-399 (1983; Zbl 0546.76072)] on the bifurcation and stability of periodic equilibrium states of a magnetic fluid subjected to a vertical magnetic field. Here the treatment is extended to cover the case of a fluid of finite depth. Conditions for the upper free surface to have hexagonal lattice structure are sought. The approach uses the Lyapunov-Schmidt method based on the analytic expansion of the potential energy.
Mathematics Subject Classification ID: 76W05
Mathematics Subject Classification ID: 35B32
zbMATH DE Number: 3956729
zbMATH Keywords: bifurcation
zbMATH Keywords: stability
zbMATH Keywords: periodic equilibrium states
zbMATH Keywords: magnetic fluid
zbMATH Keywords: vertical magnetic field
zbMATH Keywords: fluid of finite depth
zbMATH Keywords: upper free surface
zbMATH Keywords: hexagonal lattice structure
zbMATH Keywords: Lyapunov-Schmidt method
zbMATH Keywords: analytic expansion of the potential energy
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 3956729