Rendering Maxwell Equations into the Compressible Inviscid Fluid Dynamics Form

• Published in: Fluids (Basel) Vol. 8; no. 11; p. 284
• Main Author: Vadasz, Peter
• Format: Journal Article
• Language: English
• Published: Basel MDPI AG 01.11.2023
• Subjects: Charged particles; Compressibility; compressible flow; Elastic waves; Electric fields; Electromagnetism; Equivalence; Fluid dynamics; Fluid flow; Hydrodynamics; Invariants; inviscid flow; Magnetic fields; Mathematical analysis; Maxwell equations; Maxwell's equations; Navier-Stokes equations; Partial differential equations; Tests, problems and exercises; Velocity; Viscosity; United States
• ISSN: 2311-5521; 2311-5521
• DOI: 10.3390/fluids8110284

Maxwell equations governing electromagnetic effects are being shown to be equivalent to the compressible inviscid Navier–Stokes equations applicable in fluid dynamics and representing conservation of mass and linear momentum. The latter applies subject to a generalized Beltrami condition to be satisfied by the magnetic field. This equivalence indicates that the compressible inviscid Navier–Stokes equations are Lorentz invariant as they derive directly from the Lorentz-invariant Maxwell equations subject to the same Beltrami condition, provided the pressure wave propagates at the speed of light, i.e., vo=co. In addition, the derivation and results provide support for the claim that electromagnetic potentials have physical significance as demonstrated by Aharonov–Bohm effect, and are not only a convenient mathematical formulation.