6533b871fe1ef96bd12d1a86
RESEARCH PRODUCT
On the convexity of relativistic ideal magnetohydrodynamics
José-maría MartíMiguel A. AloyJ. M. IbanezJ. A. MirallesIsabel Cordero-carriónsubject
Physics[PHYS]Physics [physics]Special relativityPhysics and Astronomy (miscellaneous)Equation of state (cosmology)Degenerate energy levelsFOS: Physical sciencesGeneral Relativity and Quantum Cosmology (gr-qc)Special relativityGeneral Relativity and Quantum CosmologyConvexityMagnetic field83A05 76W05 35L60 35L65Nonlinear systemConvexityMagnetohydrodynamicsFlow (mathematics)Magnetohydrodynamics[PHYS.ASTR]Physics [physics]/Astrophysics [astro-ph]ComputingMilieux_MISCELLANEOUSMathematical physicsAstronomía y Astrofísicadescription
We analyze the influence of the magnetic field in the convexity properties of the relativistic magnetohydrodynamics system of equations. To this purpose we use the approach of Lax, based on the analysis of the linearly degenerate/genuinely non-linear nature of the characteristic fields. Degenerate and non-degenerate states are discussed separately and the non-relativistic, unmagnetized limits are properly recovered. The characteristic fields corresponding to the material and Alfv\'en waves are linearly degenerate and, then, not affected by the convexity issue. The analysis of the characteristic fields associated with the magnetosonic waves reveals, however, a dependence of the convexity condition on the magnetic field. The result is expressed in the form of a generalized fundamental derivative written as the sum of two terms. The first one is the generalized fundamental derivative in the case of purely hydrodynamical (relativistic) flow. The second one contains the effects of the magnetic field. The analysis of this term shows that it is always positive leading to the remarkable result that the presence of a magnetic field in the fluid reduces the domain of thermodynamical states for which the EOS is non-convex.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2015-05-07 |