Connection between Euler hydrodynamics and charged fluid dynamics

It is shown that the Euler hydrodynamics for vortical flows of an ideal incompressible fluid coincides with the equations of motion for a charged compressible fluid moving due to a self-consistent electromagnetic field. Transition to the Lagrangian description in a new hydrodynamics is equivalent for the original Euler equations to the mixed Lagrangian–Eulerian description — the vortex line representation. The correspondence with the charged hydrodynamics can be established also for the Euler equations for compressible fluids without pressure. This allows one to construct exact solutions for the charged three-dimensional hydrodynamics.