Convex covariant entropy density, symmetric conservative form, and shock waves in relativistic magnetohydrodynamics

Abstract

The system of conservation laws governing the relativistic magnetohydrodynamics (MHD) is shown to possess a covariant entropy density which is a convex function of suitable field variables. Therefore, the results of a general theory developed in a previous paper hold and in particular: (a) there exists a main field such that the system exhibits a conservative symmetric hyperbolic form, in the sense of Friedrichs, and therefore the local Cauchy problem is well posed in a Sobolev space Hs (s⩾4); (b) the entropy increases across a shock wave front; (c) the shock propagation velocities do not exceed the speed of light; (d) the jump of thermodynamic entropy determines the jumps of each field variable.