Maxwell's equations in divergence form for general media with applications to MHD

Details Maxwell's equations in divergence form for general media with applications to MHD Maxwell's equations in divergence form for general media with applications to MHD

Oct 1991

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1991cmaph.141...63v&link_type=abstract

Communications in Mathematical Physics, Volume 141, Issue 1, pp.63-77

Mathematics

Mathematical Physics

20

Scientific paper

Maxwell's equations in media with general constitutive relations are reformulated in covariant form as a system of divergence equations without constraints. Our reformulation enables us to express general electro-magneto-fluid problems as hyperbolic systems in divergence form. We illustrate this method on the MHD problem. In the absence of constraints, a general representation is derived for the characteristics form for first-order systems of quasi-linear partial differential equations in vector fields and scalars. Using this covariant formulation of characteristics, we find that the principle of covariance imposes a very rigid structure on the infinitesimally small amplitude waves in MHD. To demonstrate the power of the reformulation, we study numerically ultra-relativistic wave breaking using the divergence formulation of MHD.

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