Rendering Maxwell Equations into the Compressible Inviscid Fluid Dynamics Form
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 satis...
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| Published in | Fluids (Basel) Vol. 8; no. 11; p. 284 |
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| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
Basel
MDPI AG
01.11.2023
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| ISSN | 2311-5521 2311-5521 |
| DOI | 10.3390/fluids8110284 |
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| Abstract | 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. |
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| AbstractList | 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. 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., v[sub.o] =c[sub.o] . 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. |
| Audience | Academic |
| Author | Vadasz, Peter |
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| Cites_doi | 10.3390/fluids6030110 10.1112/plms/s1-9.1.91 10.1103/PhysRev.123.1511 10.2139/ssrn.4499000 10.1103/PhysRevLett.81.4863 10.1007/BF01701185 10.3390/fluids7010027 10.3390/fluids6070253 10.1063/1.869762 10.3390/fluids6060202 10.3390/fluids5010012 10.1103/PhysRevE.58.522 10.1103/PhysRev.115.485 10.3390/fluids6080264 10.1137/070700942 10.1007/s00348-006-0238-2 10.3390/fluids7070210 10.1007/s10455-021-09768-3 10.1063/1.1567798 10.1017/S0022377822000101 |
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| SubjectTerms | 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 |
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| Title | Rendering Maxwell Equations into the Compressible Inviscid Fluid Dynamics Form |
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