We present the derivation of the macroscopic equations for uniaxial ferrogels. In addition to the usual hydrodynamic variables for gels we introduce the magnetization and the relative rotations between the magnetization and the network as macroscopic variables. The relative rotations introduced here for a system with magnetic degrees of freedom are the analog of the relative rotations introduced by de Gennes in nematic elastomers for rotations of the director with respect to the elastomeric network. These variables give rise to a large number of static as well as dynamic effects due to their coupling to the magnetization, the strain field, and the density of linear momentum. A few of them are discussed for specific geometries, for example, the case of a shear-induced magnetization perpendicular to the preferred direction.

We present a nonlinear description of the Rosensweig instability in isotropic magnetic gels based on the energy minimizing method used by Gailitis to describe the Rosensweig instability in typical ferrofluids. We extend his discussion to media with elastic degrees of freedom, assuming the shear modulus as a perturbation to the pure fluid case. We study the relative stability of the regular planforms of stripes, squares and hexagons as a function of the elastic shear modulus.

Summary We derive the dispersion relation of surface waves for isotropic magnetic gels in the presence of an external magnetic field normal to the free surface. Above a critical field strength surface waves become linearly unstable with respect to a stationary pattern of surface protuberances. This linear stability criterion generalizes that of the Rosensweig instability for ferrofluids by taking into account elasticity, additionally.

We present a method to find the adjoint system of equations and the corresponding boundary conditions for free deformable surfaces. Motivated by the nonlinear discussion of the Rosensweig instability in ferrogels using the energy method, we treat the surface as dynamic and take the stationary limit only in the very end. We analyze the adjoint system of dynamic equations together with its corresponding boundary conditions and present as a solution the adjoint eigenvectors for the Rosensweig instability. The method is also applied to pure surface tension driven convection (Marangoni convection).

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