Abelian and non-Abelian considerations on compressible fluids with Maxwell-type equations and minimal coupling with the electromagnetic field

In this work, we have obtained Maxwell-type equations for a compressible fluid whose sources are functions of velocity and vorticity. A correlation function and the dispersion relation were analyzed as functions of the Reynolds number. A Lagrangian for the Lamb vector and the vorticity was constructed, and the equations of motion were discussed. After that, we have analyzed the case of a charged fluid dynamics. Finally, the non-Abelian generalization of some results was introduced. A basic review for non-Abelian fluids was described in Appendix B.