Q:What is the analogue of the excitation vector in the case of mass density?

[mma]

Mass density is a 3-form, just like electric charge density. Hence it's exterior derivative is 0. This implies that there is a 2-form whose exterior derivative is the density 3-form. If this density is the electric charge density, then the name of this 2-form is "excitation" (D). But what is the name of it in the case when we speak about mass density instead off electric charge density? And where is it used?

 

[mma]

Of course the above mentioned D excitation is the electric excitation (other name of it is electric displacement field). The equation which states that the exterior derivative of the electric excitation is the electric charge density is the so-called Gauss-law, and this is one of 4 the Maxwell's equations. And this equation must have a counterpart in fluid-dynamics, where the mass density plays the role of the electric charge density in this equation.

Moreover, there is another Maxwell's equation what must have a counterpart in fluid-dynamic. This is the Oersted-Ampere law. This equation follows directly from the continuity equation and from the Gauss-law. Regarding that both equations are valid not only in electrodynamics but in fluid-dynamics also, there must be a corresponding equation in fluid-dynamics, i.e. there must be a counterpart of the magnetic excitation field (H) also (this is an 1-form field).

Does anybody use these equations and quantities in fluid-dynamics?

 

[mma]

I mean eqations (3.1) and (3.2) in http://arxiv.org/abs/physics/0005084"