Abstract
one of Maxwell’s equations. The magnetic field must also satisfy ∇·B = 0. This constraint expresses the absence of magnetic monopoles, which have never been observed experimentally. Since (1) implies ∂t(∇·B) = 0 this constraint is often treated as an initial condition, which will be preserved under subsequent evolution. The induction equation (1) is combined with the equations of gas dynamics to describe the behaviour of compressible electrically conducting fluids subject to magnetic fields. For non-relativistic fluids, where Maxwell’s displacement current may be neglected, the combined system is referred to as the magnetohydrodynamic (MHD) equations. The compressible ideal (inviscid and perfectly conducting) MHD equations may be written as a hyperbolic system of conservation laws in the form [7, 9, 11]
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