Magnetohydrodynamic Shock Waves

Abstract

A state Y of the system (fluid + field) at the point × of V ₄ is defined by the values of p, S, u, h (eight parameters). Over a domain Ω of V ₄, a magnetohydrodynamic shock wave is a solution of the fundamental system in a weak sense such that there exists a hypersurface Σ, the wave front, satisfying the following conditions

• 1) On both sides of Σ, that is over Ω⁺ and Ω⁻, the states are C¹ — functions of × and the fundamental system is satisfied in the usual sense.

• 2) The variables defining the states are regularly discontinuous at the traverse of Σ, and in the neighborhood of Σ, the fundamental system is satisfied in the sense of distributions.