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

TL;DR

This paper derives Maxwell-like equations for compressible fluids influenced by electromagnetic fields, explores their properties through correlation functions and dispersion relations, and extends the analysis to non-Abelian fluids, providing new theoretical insights.

Contribution

It introduces Maxwell-type equations for compressible fluids with electromagnetic coupling and generalizes the framework to non-Abelian fluids, expanding the theoretical understanding.

Findings

Maxwell-type equations derived for compressible fluids with electromagnetic sources

Dispersion relations analyzed as a function of Reynolds number

Non-Abelian generalization of fluid dynamics equations introduced

Abstract

In this work we have obtained Maxwell-type equations for a compressible fluid which sources are functions of velocity and vorticity. A correlation function and the dispersion relation were analyzed as function 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 the Appendix.