Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5500273 | Physica D: Nonlinear Phenomena | 2017 | 28 Pages |
Abstract
We establish the existence of spatially localised one-dimensional free surfaces of a ferrofluid near onset of the Rosensweig instability, assuming a general (nonlinear) magnetisation law. It is shown that the ferrohydrostatic equations can be derived from a variational principle that allows one to formulate them as an (infinite-dimensional) spatial Hamiltonian system in which the unbounded free-surface direction plays the role of time. A centre-manifold reduction technique converts the problem for small solutions near onset to an equivalent Hamiltonian system with finitely many degrees of freedom. Normal-form theory yields the existence of homoclinic solutions to the reduced system, which correspond to spatially localised solutions of the ferrohydrostatic equations.
Keywords
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Physical Sciences and Engineering
Mathematics
Applied Mathematics
Authors
M.D. Groves, D.J.B. Lloyd, A. Stylianou,