Etude des Equations des Fluides Chargés Relativistes Inductifs et Conducteurs

Abstract

In the first part a system of equations for an inductive charged relativistic fluid with finite conductivity is written in a space time with given metric, taking into account thermodynamic phenomena. Speeds of propagation of various types of waves are determined under a restrictive hypothesis concerning the heat currentq: thatq depends only on the thermodynamical quantities and the gradient of one function of these quantities.

In the second part it is shown, by a detailed study of the characteristic polynomial and of its irreducible factors, that, whenq is negligible, the proposed system is non-strictly hyperbolic in the sense ofJ. Leray andY. Ohya and existence and uniqueness theorems of a certain Gevrey class are verified; the relativistic causality principle is satisfied under some physically reasonable assumptions on the thermodynamical quantities. The system becomes strictly hyperbolic (existence and uniqueness theorems obtain in classes of functions with a finite number of derivatives) when the fluid is both non inductive and of zero electrical conductivity.

In the third part we show briefly, by the methods of the second part, that the equations of relativistic fluids, with an infinite electrical conductivity is also non-strictly hyperbolic. The linearized equations (in the neighborhood of constant values) are strictly hyperbolic.