Uniqueness in MHD in divergence form: right nullvectors and well-posedness

Details Uniqueness in MHD in divergence form: right nullvectors and well-posedness Uniqueness in MHD in divergence form: right nullvectors and well-posedness

1998-04-14

arxiv.org/abs/astro-ph/9804139v2

J.Math.Phys. 43 (2002) 6195-6208

Astronomy and Astrophysics

Astrophysics

To appear in J Math Phys

Scientific paper

10.1063/1.1510174

Magnetohydrodynamics in divergence form describes a hyperbolic system of covariant and constraint-free equations. It comprises a linear combination of an algebraic constraint and Faraday's equations. Here, we study the problem of well-posedness, and identify a preferred linear combination in this divergence formulation. The limit of weak magnetic fields shows the slow magnetosonic and Alfven waves to bifurcate from the contact discontinuity (entropy waves), while the fast magnetosonic wave is a regular perturbation of the hydrodynamical sound speed. These results are further reported as a starting point for characteristic based shock capturing schemes for simulations with ultra-relativistic shocks in magnetized relativistic fluids.

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