On incompressible magnetohydrodynamic equations in terms of differential forms

Magnetohydrodynamic offers examples of non-scalar advection-diffusion problems which are relevant for applications. We consider its formulation in terms of differential forms, with the presence of operators such as the exterior derivative and Lie's derivative, being aware of the underneath analogy between electromagnetic dynamic and incompressible fluid dynamic. We analyze the intrinsic structure of the magnetic and fluid coupling, with a special attention to the Laplace's force. Taking the cue from [11] we focus on the density of virtual power associated with each of the involved forces.