Fluid-dynamic formulation of Maxwell´s equations

Many phenomena in electricity and magnetism have been storically interpreted using fluid-dynamic analogies, e.g., electricity was seen like a fluid “current” of some kind. J. C. Maxwell himself interpreted magnetic field as originated by vortex of (electric) current and electromagnetic waves were considered travelling through an elastic fluid called “aether”[1]. At the end of XIX century researchers in Fluid-dynamics and Electromagnetism began to separate their objectives, developing different methods and notations and nowadays their fields looks quite distant. In this article a suitable Fluid-dynamic reformulation of Maxwell´s equations will be presentes, in particular drawing out a system of hyperbolic equations that can be tackled with Riemann´s method. More in general, the unification of notations in Electromagnetic and Fluid-dynamics could bring to significative advantages in both these fields, extending the results from one discipline to the other one.