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

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