Bifurcation and stability of cellular states in magnetic fluids (Q1077304)

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.