IJPAMR International Journal of Pure and Applied Mathematics Research 2789-9160 SvedbergOpen ijpamr-1-1-001 10.51483/IJPAMR.1.1.2021.1-20 Research Paper A New Model for Polyatomic Gases in an Electromagnetic Field S.Pennisi 1 * 1Dipartimento di Matematica ed Informatica, Universit’a di Cagliari, Cagliari, Italy. E-mail: spennisi@unica.it *Corresponding author: S. Pennisi, Dipartimento di Matematica ed Informatica, Universit’a di Cagliari, Cagliari, Italy. E-mail: spennisi@unica.it 10 2021 1 1 1 20 Abstract

Significant progress has recently been made in the field of polyatomic gases, in particular by Professors T Ruggeri, M Sugiyama and collaborators. But so far it has not yet been seen how they interact with an electromagnetic field. This is realized in the present paper. As a first step, we consider here the case when the gas is described only by the Euler Equations and the electromagnetic field by Maxwell’s Equations in materials. To find the field equations, a supplementary conservation law is imposed which is the entropy principle for the Euler Equations, while for Maxwell’s Equations is the energy; this is useful because in this way the whole set of equations becomes a symmetric hyperbolic system as usual in Extended Thermodynamics. One of the results is a restriction on the law connecting the magnetic field in the empty space and the electric field in materials to the electromotive force and its dual: they are the gradients of a scalar function. Obviously, two Maxwell’s equations are not evolutive (The Gauss magnetic and electric laws).

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