On a degenerate boundary value problem to relativistic magnetohydrodynamics with a general pressure law

Rahul Barthwal; T. Raja Sekhar

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arXiv · 2306.13974

On a degenerate boundary value problem to relativistic magnetohydrodynamics with a general pressure law

Rahul Barthwal·T. Raja Sekhar

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Abstract

This work is concerned with establishing the existence and uniqueness of the solution to a mixed-type degenerate boundary value problem for a relativistic magnetohydrodynamics system. We first consider a full relativistic magnetohydrodynamics system and reduce it to a simplified form under the assumption that the magnetic field vector is orthogonal to the velocity vector. We consider a boundary value problem for the steady part of this reduced system where the boundary data is prescribed on a sonic boundary and a characteristic curve. Here the main difficulty is the consideration of a relativistic system, with a general equation of state while considering the magnetic field effects as well, which we believe has never been analyzed before in the context of the analytical study of sonic-supersonic flows. Also, the degeneracy of the governing equations along the sonic curve is a crucial challenge. However, we employ the iteration method used in the work of Li and Hu \cite{li2019degenerate} to prove the existence and uniqueness of a local classical supersonic solution in the partial hodograph plane first and finally, we recover a local smooth solution to the boundary value problem in the physical plane by applying an inverse transformation.

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Rahul Barthwal, T. Raja Sekhar. 2023-06-24. On a degenerate boundary value problem to relativistic magnetohydrodynamics with a general pressure law. https://arxiv.org/abs/2306.13974

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